Abstract

Fluorescence molecular tomography (FMT) has been a promising imaging tool because it allows an accurate localizaton and quantitative analysis of the fluorophore distribution in animals. It, however, is still a challenge since its reconstruction suffers from severe ill-posedness. This paper introduces a reconstruction frame based on three-way decisions (TWD) for the inverse problem of FMT. On the first stage, a reconstruction result on the whole region is obtained by a certain reconstruction algorithm. With TWD, the recovered result has been divided into three regions: fluorescent target region, boundary region, and background region. On the second stage, the boundary region and fluorescent target region have been combined into the permissible region of the target. Then a new reconstruction on the permissible region has been carried out and a new recovered result is obtained. With TWD again, the new result has been classified into three pairwise disjoint regions. And the new fluorescent target region is the final reconstructed result. Both numerical simulation experiments and a real mouse experiment are carried out to validate the feasibility and potential of the presented reconstruction frame. The results indicate that the proposed reconstuction strategy based on TWD can provide a good performance in FMT reconstruction.

© 2018 Optical Society of America

1. INTRODUCTION

As a promising optical molecular imaging tool, fluorescence molecular tomography (FMT) has the advantages of high sensitivity, low cost, non-invasiveness, non-ionization, and so on [1,2]. It has gained a great deal of attention from researchers. Since it allows fast resolving of the three-dimensional visualization of fluorophore within small animals in vivo, FMT has been successfully applied in cancer diagnosis, drug development, and therapeutics assessment [14].

However, its reconstruction is a highly ill-posed inverse problem [5]. In order to obtain a stable and meaningful solution, researchers developed a variety of strategies for FMT. Regularization is typically used to tackle the inverse problem, such as well-known Tikhonov regularization [6,7] and sparisty regularization [8,9]. In [10], Jiang et al. have proposed a novel l2,1-norm optimization for FMT. The method not only achieves accurate and desirable fluorescent source reconstruction, but also demonstrates enhanced robustness to noise. In [11,12], the authors present a modified nonlinear anisotropic diffusion regularization method, which is called patch-based anisotropic diffusion with wavelet patch compression, for FMT reconstruction. This new method has the ability to preserve important features in the reconstructions. In [13], Mohajerani et al. have proposed a Fuzzy inference system for the minimization of FMT, which does not need to set the regularization parameters. In addition, some hybrid imaging systems, which combine other imaging modalities with FMT, have been designed. They provide priori information and further improve the reconstruction accuracy [6,7,1418]. For example, anatomical information from the anatomical imaging modalities in the form of priors has also been incorporated into the inversion problem to improve the solutions. In particular, x-ray computed tomography (CT) has been combined with FMT, which is referred to as FMT-XCT [6,17,18]. The permissible region has also been employed to speed up the reconstruction and improve the quality of solutions [1921]. However, the extraction of the permissible region is based on the two-decision theory; namely, the reconstruction region is divided into the permissible region and the non-permissible region. In this paper, we developed a reconstruction frame for FMT based on three-way decisions (TWD). This frame not only provides a permissible region but also allows a post-process of the recovered results. A numerical simulation experiment and an in vivo experiment on a small mouse are carried out to test the feasibility and potential of the reconstruction frame.

This paper is organized as follows. The inverse problem of FMT, TWD theory, and reconstruction frame based on TWD are presented in Section 2. In Section 3, a numerical simulation experiment and small animal experiment are conducted to test the frame. Finally, we discuss the results and present a conclusion in Section 4.

2. RELATED WORK

A. Reconstruction Problem

Usually, the near-infrared photon propagation in biological tissues has the characteristics of high scattering and low absorption. In a continuous-wave form, two coupled diffusion equations, the lower-order approximation of the radiative transport equation, are used to describe the propagation of excitation and emission light in tissue [1,5]:

{·(Dx(r)ϕx(r))+μax(r)ϕx(r)=Θδ(rrs)·(Dm(r)ϕm(r))+μam(r)ϕm(r)=ϕx(r)ημaf(r)(rΩ),
where Ω is the domain of the position vector r and rs is the excitation source position. Subscripts x and m denote excitation and emission light, respectively. D(r) is the diffusion coefficient, and μa(r) is the absorption coefficient. ϕ(r) denotes the photon density. ημaf(r) is the fluorescent yield to be reconstructed, which is denoted as X(r) in the following part of this article. Θ denotes the amplitude of the point excitation source. Here, the Robin-type boundary condition is utilized for the boundary conditions [22]. Equation (1) is solved using the finite element method and then the FMT problem can be linearized as the following weight matrix equation:
ϕmmeas=AX,whereX0,
where A is the weight matrix, ϕmmeas is the fluorescence intensity, and X is the fluorescent target to be reconstructed. Detailed descriptions can be found in [13,19].

In general, the regularized least-squares formation is utilized for the reconstruction as follows:

X=argminX0,XΩ{AXϕmmeas22+λXq},
where λ is the regularization coefficient and q(0,2]. If q=2, the Tikhonov regularization term is employed [6,7]. If q=1, Eq. (3) is a sparsity regularization problem [8,9].

B. Three-Way Decisions

TWD has attracted a growing interest in exploring various theories and models since it was proposed by Yao [23]. A TWD model is an extension of the traditional binary-decision model, which adds a third option. The idea of TWD is generated from decision-theoretic rough set (DTRS) [24]. Intuitively, the universe is divided into three pairwise disjoint regions: positive, negative, and boundary regions by two thresholds α and β of DTRS. The two-way decisions have only two kinds of actions: positive and negative. And the positive decision in the positive region makes the decision of acceptance. The negative decision in the negative region makes the decision of rejection. Compared to the two-way decision method including acceptance and rejection decisions only, TWD has an additional deferment decision, which is generated from the boundary region. As an effective way to deal with uncertain problems, TWD has been widely used in decision making. Jia and Shang have made a comparative study of TWD and two-way decisions on filtering spam email [25]. Li et al. proposed a TWD framework for cost-sensitive software defect prediction [26]. Savchenko has presented a fast multi-class recognition of piecewise regular objects based on sequential TWD and granular computing [27]. TWD has also been employed in multiple attribute group decision making [28]. For FMT reconstruction, there was no post-processing strategy for the recovered results. In general, the recovered images have spurious information which might mislead users and produce false information. The TWD idea implies that the reconstructed results can be further classified into three pairwise disjoint subparts: target (positive region), background (negative region), and boundary regions. The target region means it has a high probability to contribute to the fluorophore (fluorescent target). The background indicates that it makes very low probability contribution to the fluorescent target distribution. And the nodes in the boundary region either belong to the fluorescent target region or belong to the background region. More information needs to be added to make a clear decision. So a permissible region of a fluorescent target can be extracted by combining the target region with the background region. And an algorithm frame based on TWD for FMT is described in detail in Section 2.C.

C. Algorithm Frame Based on Three-Way Decisions for FMT

First, a whole region reconstruction is carried out and the recovered results are divided into three pairwise disjoint regions by two thresholds α and β based on three-way decisions. The nodes in the positive region are labeled as fluorescent target, the nodes in the negative are denoted as background, and the nodes in the boundary are deferred for further exam. The nodes in the boundary region either belong to the fluorescent target or belong to the background region. More information needs to be added to make a clear decision. Here, the information may be deduced from the known conditions or by other means. However, it can be sure that the measured data on the surface of the object are created by nodes in both the fluorescent target region and boundary region. So nodes in the two regions are considered as a permissible region of the fluorescent target. The background points, which make very low probability contribution in the fluorescent target distribution, are omitted. After this processing, the variable X is limited to the permissible region. We define a vector P¯, which is a columns vector composed of zero or unity elements, as follows:

P¯={1if nodei is within the permissible region0otherwise.
Then, the A and X in Eq. (2) become A=AP¯ and X=XP¯, and represents the operation that removes columns in matrix A corresponding with the zero-element in column vector P¯. Then the minimization problem of Eq. (3) is converted into the following form:
X=argminX0,XPR{AXϕmmeas22+λXp},
where PR is the permissible region. On the second stage, a new reconstruction is carried out on the permissible region to obtain a new recovered result. With TWD again, new fluorescent target, background, and boundary regions are obtained by TWD. The fluorescent target region is the final reconstructed result. Figure 1 shows the flow chart of the proposed method for FMT.

3. EXPERIMENTS

In this section, a numerical simulation experiment and real mouse experiment are implemented to test the performance of the reconstruction frame based on TWD.

A. Numerical Simulation Experiment

A non-uniform cylinder model is utilized to carry out the simulation experiments. The cylinder radius is 10 mm, with a high of 30 mm, which is composed of five organs: (1) muscle, (2) heart, (3) lungs, (4) liver, and (5) kidneys. The purpose of the small cylinder with a radius of 0.5 mm, high of 1.5 mm, is to imitate the fluorescent target. Its center coordinate is (0.0, 6.0, 15.0) mm, which is located in the lungs. The optical properties are the same as those presented in [19]. Figure 2 is the model of single fluorescent target reconstruction. The actual fluorescence yield is set to be 0.05mm1. The fluorescent target was excited by 18 point sources at different positions in sequence, and the field of view of the detection with respect to each excitation source is 120°. For the inverse problem, a mesh with 5545 nodes and 30,636 tetrahedral elements is the reconstruction mesh. To evaluate the quality of the recovered images, localization error (LE) and normalized root mean square error (nRMSE) are adopted in this study [19]. In general, a high-quality reconstructed image possesses LE and nRMSE values close to 0.

 figure: Fig. 1.

Fig. 1. Flow chart of the reconstruction strategy based on three-way decisions.

Download Full Size | PPT Slide | PDF

 figure: Fig. 2.

Fig. 2. Model of single fluorescent target reconstruction, which includes five organs and a target.

Download Full Size | PPT Slide | PDF

The theory of TWD proposed by Yao is constructed based on the notions of the acceptance, rejection, and deferment, which can be directly generated by the three regions of probabilistic rough sets. For the fluorescent target recognition of FMT, the detail of representing TWD is summarized in Table 1. The cost function matrix of TWD is shown in Table 2.

Tables Icon

Table 1. TWD for Fluorescent Target Recognition of FMT

Tables Icon

Table 2. Cost Function Matrix for Fluorescent Target Prediction Based on TWD

And the threshold parameters α and β (0α<β1) are defined by the following formula: β=(λPNλBN)(λPNλBN)+(λBPλPP), α=(λBNλNN)(λBNλNN)+(λNPλBP). This means that these two parameters are determined by the costs function. In this case, we obtained the following rules:

(P)Ifp(T|t)β,decidetPOS(T);(B)Ifα<p(T|t)<β,decidetBND(T);(N)Ifp(T|t)α,decidetNEG(T).
In the FMT problem, we only obtained the fluorescent yield of each node. The normalized value of the fluorescent yield is considered as conditional probability. However, the cost function of FMT reconstruction is unknown, and there are no other methods to the pair of thresholds in current three-way decision theory. Thus, we cannot use the above formula to compute the two thresholds. For simplicity, we define α and β(α<β) in this work as 20% and 80%, respectively, which are two values often used for FMT reconstruction.

In this work, we considered q=1 and q=2 in Eq. (3). When q=1, gradient projection for sparse reconstruction (GPSR) is usually employed to solve the sparsity regularization problem [29]. If q=2, conjugate gradient least squares (CGLS) is utilized for the Tikhonov regularization problem [30]. Incomplete variables truncated conjugate gradient (IVTCG), which was developed in our previous work, has also been successfully applied in FMT [30]. To make a comparative study on the reconstruction, this work showed the recovered results by these three methods combined with TWD and without TWD.

Figure 3 and Table 3 show results of single target reconstruction. Figures 3(a), 3(d), and 3(g) show the 2D views of the recovered results by IVTCG, CGLS, and GPSR with no post-processing, respectively. Figures 3(c), 3(f), and 3(i) present the results by IVTCG+TWD, CGLS+TWD, and GPSR+TWD. Figures 3(b), 3(e), and 3(h) are the results by IVTCG, CGLS, and GPSR with artificial threshold. In general, when the original recovered results of FMT, containing spurious information, are directly provided to users without post-processing, it is likely to mislead users. In [29], we presented the recovered results by selecting nodes with a threshold of 70% of the maximum value by manual experience. And in [31], we developed an adaptive threshold method for recovered images of FMT. Both of these two strategies can only remove the artifacts with smaller values, but they cannot modify the recovered results; please see Table 3. However, TWD not only provides a permissible region of target, which further improves the recovered results (see Table 3), but also removes the spurious information. According to Fig. 3 and Table 3, the location errors of the fluorescent target are smaller by using a permissible region extracted by TWD. And nRMSEs are smaller than those of methods with no TWD.

 figure: Fig. 3.

Fig. 3. First row shows the 2D views (z=15mm) of the reconstructed results by IVTCG with no post-processing, IVTCG+artificial threshold and IVTCG+TWD. Second row shows the 2D views (z=15mm) by CGLS with no post-processing, CGLS+artificial threshold and CGLS+TWD. Third row shows the 2D views (z=15mm) of results by GPSR with no post-processing, GPSR+artificial threshold and GPSR+TWD.

Download Full Size | PPT Slide | PDF

Tables Icon

Table 3. Quantitative Analysis of Single Target Reconstruction Results

A relationship between the recovered results with TWD and the number of excitation points (3, 6, and 9) has been presented. Table 4 shows that the accuracy is improved with the increase of the number of excitation points. This is mainly because the scale of fluorescence measurement increases when the number of excitation points raises, which reduces the ill-posedness of the inverse problem to a certain extent. And nine excitation points can obtain satisfactory reconstruction results.

Tables Icon

Table 4. Quantitative Analysis of the Reconstruction Results of IVTCG+TWD under Different Excitation Points

Because of the severe ill-posedness of the inverse problem, it is difficult to get a stable solution. In order to study the effect of noise on the reconstruction results, a comparison test of 5%, 10%, 15%, 20%, and 25% noise levels is designed to verify the stability of the method. The different levels of the Gaussian noise are added on the surface measurements by the formula ϕ¯m=ϕm+δn, where ϕm is the surface measure data and δ is the noise level parameter (5%, 10%, 15%, 20%, and 25%). And n is a random error generated by a MATLAB function randn; its standard deviation is ϕm2/Num, where ϕm2 is the l2 norm of ϕm and Num is the number of surface measured nodes. This noise is similar to the noise caused by the dark current of the CCD camera in the physical experiment. The quantitative analysis is shown in Fig. 4. After adding different proportions of noise, the location errors and nRMSEs have a slight fluctuation, which indicates that the IVTCG+TWD has good stability and noise immunity. In addition, it is obvious that the proposed algorithm provides better recovered results with smaller LE and nRMSE according to Fig. 4.

 figure: Fig. 4.

Fig. 4. Reconstruction results of IVTCG and IVTCG+TWD methods under different proportions of noise levels. (a) The location errors with different noise levels. (b) The nRMSEs with different noise levels.

Download Full Size | PPT Slide | PDF

B. Real Implanted Experiments

We further assess the performance of the TWD with in vivo small animal experimental data. The experiment data was collected from the FMT/micro-CT dual-mode system on adult nude mice; the mice were scanned with micro-CT [30]. We show the torso section of the mice with a height of 41 mm in Fig. 5(a). The main organs of the experimental mice included muscle, lung, heart, stomach, liver, and kidney organs. The optical parameters of the organs are consistent with the literature [30]. The purpose of the cylinder, implanted at (20.2, 27.8, and 7.4 mm), is to mimic the fluorescence target. Figure 5(b) shows the vertical view of the fluorescent target at z=7.4mm. It is 6.4 mm away from the surface along the x-axis and 5.0 mm away from the surface along the y-axis. The depth of the fluorescent target in tissue is about 4.7 mm, as shown in Fig. 5(b). The cylinder contains Cy5.5 solution at a concentration of 4000 nM. Figure 6 and Table 5 display the results. The reconstruction frame based on TWD made an improvement on results from the third column images of Fig. 6. The LE and nRMSE were smaller with the proposed reconstruction frame in Table 5.

 figure: Fig. 5.

Fig. 5. (a) Anatomical structure of real mice. (b) Vertical view of the fluorescent target at z=7.4mm.

Download Full Size | PPT Slide | PDF

 figure: Fig. 6.

Fig. 6. First row shows the 2D views (x=20.2mm) of the reconstructed results by IVTCG with no post-processing, IVTCG+artificial threshold and IVTCG+TWD. Second row shows the 2D views (x=20.2mm) by CGLS with no post-processing, CGLS+artificial threshold and CGLS+TWD. Third row shows the 2D views (x=20.2mm) of results by GPSR with no post-processing, GPSR+artificial threshold and GPSR+TWD.

Download Full Size | PPT Slide | PDF

Tables Icon

Table 5. Quantitative Analysis of Experimental Reconstruction Results of Real Mice

4. DISCUSSION AND CONCLUSIONS

This work presents a reconstruction frame for FMT based on TWD. Different from the traditional two decisions, the two threshold values of TWD divide the recovered results into three pairwise disjoint regions: the target region, the boundary region, and the background region. Intuitively, the target region is the fluorescent target region which we are interested in. The nodes in the boundary region either belong to the fluorescent target or do not belong to it. If one wants to know the exact classification, more information needs to be added. However, it is natural to combine the boundary region with the target region to form a permissible region of fluorescent target. Then, a new reconstruction can be carried out on the permissible region. Here, the TWD provides a permissible region for reconstruction. This is the first time that we used TWD. In theory, the permissible region can reduce the number of variables, which reduces the ill-posedness of the problem and improves the image quality. For the recovered results in the permissible region, three new pairwise disjoint regions would be obtained by TWD, namely, the target region, the boundary region, and the background region. This is the second time that we used TWD. From the reconstruction frame, it is known that the TWD idea has been used twice. The first time is to extract the permissible region. The second time is to post-process the recovered results, which provides the target clearly.

To test the performance of the reconstruction frame based on the TWD, simulaiton experiments and in vivo experiments are carried out in the work. The IVTCG, GPSR, and CGLS are employed as reconstruction methods. The experiments demonstrated that the recovered images with the proposed frame are better than those of ones without the proposed strategy according to LE and nRMSE.

In TWD theory, the threshold values α and β are very important because they determine the division of the three regions. The threshold parameters are related to cost functions, which are unknown in FMT. Then, we cannot give the calculation formula of the threshold parameters in the current TWD theory. With the development of the theory, multiple ways will be developed for them. In this work, they are defined as 20% and 80% by experience, respectively. Our future work will be focused on investigating how to determine the pair of thresholds, which is important to both three-way decision theory and the FMT reconstruction problem.

It is challenging work to get a shape of the target in FMT. But, according to the TWD, the boundary region should contain the boundary of the target, which provides a possible way to delineate the three-dimensional boundary of the target. The shape of the target can be used to guide the radiation therapy further, which is a meaningful issue. This is also our future work.

Funding

Natural Science Foundation of Shaanxi Province (2017JM1036, 2017JQ6006, 2017JQ6017, 2018JQ6099); China Postdoctoral Science Foundation (2016M602851); National Natural Science Foundation of China (NSFC) (11571012, 61701403, 61772019).

REFERENCES

1. C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014). [CrossRef]  

2. V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002). [CrossRef]  

3. C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015). [CrossRef]  

4. S. Kumar and R. Richards-Kortum, “Optical molecular imaging agents for cancer diagnostics and therapeutics,” Nanomedicine 1, 23–30 (2017). [CrossRef]  

5. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Prob. 15, R41–R93 (1999). [CrossRef]  

6. R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010). [CrossRef]  

7. B. Q. Li, F. Maafi, R. Berti, P. Pouliot, E. Rhéaume, J. C. L. Tardif, and F. Lesage, “Hybrid FMT-MRI applied to in vivo atherosclerosis imaging,” Biomed. Opt. Express 5, 1664–1676 (2014). [CrossRef]  

8. J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016). [CrossRef]  

9. J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014). [CrossRef]  

10. S. X. Jiang, J. Liu, Y. An, G. L. Zhang, J. Z. Ye, Y. M. Mao, K. S. He, C. W. Chi, and J. Tian, “Novel l2, 1-norm optimization method for fluorescence molecular tomography reconstruction,” Biomed. Opt. Express 7, 2342–2359 (2016). [CrossRef]  

11. T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 1: technical principles,” Phys. Med. Biol. 61, 1439–1451 (2016). [CrossRef]  

12. T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction,” Phys. Med. Biol. 61, 1452–1475 (2016). [CrossRef]  

13. P. Mohajerani and V. Ntziachristos, “An inversion scheme for hybrid fluorescence molecular tomography using a Fuzzy inference system,” IEEE Trans. Med. Imaging 35, 381–390 (2016). [CrossRef]  

14. Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014). [CrossRef]  

15. S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011). [CrossRef]  

16. P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015). [CrossRef]  

17. A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012). [CrossRef]  

18. M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014). [CrossRef]  

19. H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016). [CrossRef]  

20. J. Zhang, J. Shi, X. Cao, F. Liu, J. Bai, and J. Luo, “Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy,” J. Opt. Soc. Am. A 31, 1886–1894 (2014). [CrossRef]  

21. M. A. Naser and M. S. Patterson, “Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography, normalized data, and optimized selection of the permissible source region,” Biomed. Opt. Express 2, 169–184 (2011). [CrossRef]  

22. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995). [CrossRef]  

23. Y. Yao, “Three-way decision: an interpretation of rules in rough set theory,” in International Conference on Rough Sets and Knowledge Technology, P. Wen, Y. Li, L. Polkowski, Y. Yao, S. Tsumoto, and G. Wang, eds. (Springer, 2009), pp. 642–649.

24. Y. Yao, “The superiority of three way decision in probabilistic rough set models,” Inf. Sci. 181, 1080–1096 (2011). [CrossRef]  

25. X. Jia and L. Shang, “Three-way decisions versus two-way decisions on filtering spam email,” in Transactions on Rough Sets XVIII, J. Peters, A. Skowron, T. Li, Y. Yang, J. Yao, and H. Nguyen, eds. (Springer, 2014), pp. 69–91.

26. W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016). [CrossRef]  

27. A. Savchenko, “Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing,” Knowledge-Based Syst. 91, 252–262 (2016). [CrossRef]  

28. B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018). [CrossRef]  

29. M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007). [CrossRef]  

30. H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013). [CrossRef]  

31. H. Yi, H. Wei, J. Peng, Y. Hou, and X. He, “Adaptive threshold method for recovered FMT,” J. Opt. Soc. Am. A 35, 256–261 (2018). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
    [Crossref]
  2. V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
    [Crossref]
  3. C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
    [Crossref]
  4. S. Kumar and R. Richards-Kortum, “Optical molecular imaging agents for cancer diagnostics and therapeutics,” Nanomedicine 1, 23–30 (2017).
    [Crossref]
  5. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Prob. 15, R41–R93 (1999).
    [Crossref]
  6. R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
    [Crossref]
  7. B. Q. Li, F. Maafi, R. Berti, P. Pouliot, E. Rhéaume, J. C. L. Tardif, and F. Lesage, “Hybrid FMT-MRI applied to in vivo atherosclerosis imaging,” Biomed. Opt. Express 5, 1664–1676 (2014).
    [Crossref]
  8. J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
    [Crossref]
  9. J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
    [Crossref]
  10. S. X. Jiang, J. Liu, Y. An, G. L. Zhang, J. Z. Ye, Y. M. Mao, K. S. He, C. W. Chi, and J. Tian, “Novel l2, 1-norm optimization method for fluorescence molecular tomography reconstruction,” Biomed. Opt. Express 7, 2342–2359 (2016).
    [Crossref]
  11. T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 1: technical principles,” Phys. Med. Biol. 61, 1439–1451 (2016).
    [Crossref]
  12. T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction,” Phys. Med. Biol. 61, 1452–1475 (2016).
    [Crossref]
  13. P. Mohajerani and V. Ntziachristos, “An inversion scheme for hybrid fluorescence molecular tomography using a Fuzzy inference system,” IEEE Trans. Med. Imaging 35, 381–390 (2016).
    [Crossref]
  14. Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
    [Crossref]
  15. S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
    [Crossref]
  16. P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
    [Crossref]
  17. A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
    [Crossref]
  18. M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
    [Crossref]
  19. H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
    [Crossref]
  20. J. Zhang, J. Shi, X. Cao, F. Liu, J. Bai, and J. Luo, “Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy,” J. Opt. Soc. Am. A 31, 1886–1894 (2014).
    [Crossref]
  21. M. A. Naser and M. S. Patterson, “Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography, normalized data, and optimized selection of the permissible source region,” Biomed. Opt. Express 2, 169–184 (2011).
    [Crossref]
  22. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
    [Crossref]
  23. Y. Yao, “Three-way decision: an interpretation of rules in rough set theory,” in International Conference on Rough Sets and Knowledge Technology, P. Wen, Y. Li, L. Polkowski, Y. Yao, S. Tsumoto, and G. Wang, eds. (Springer, 2009), pp. 642–649.
  24. Y. Yao, “The superiority of three way decision in probabilistic rough set models,” Inf. Sci. 181, 1080–1096 (2011).
    [Crossref]
  25. X. Jia and L. Shang, “Three-way decisions versus two-way decisions on filtering spam email,” in Transactions on Rough Sets XVIII, J. Peters, A. Skowron, T. Li, Y. Yang, J. Yao, and H. Nguyen, eds. (Springer, 2014), pp. 69–91.
  26. W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016).
    [Crossref]
  27. A. Savchenko, “Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing,” Knowledge-Based Syst. 91, 252–262 (2016).
    [Crossref]
  28. B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
    [Crossref]
  29. M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
    [Crossref]
  30. H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
    [Crossref]
  31. H. Yi, H. Wei, J. Peng, Y. Hou, and X. He, “Adaptive threshold method for recovered FMT,” J. Opt. Soc. Am. A 35, 256–261 (2018).
    [Crossref]

2018 (2)

B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
[Crossref]

H. Yi, H. Wei, J. Peng, Y. Hou, and X. He, “Adaptive threshold method for recovered FMT,” J. Opt. Soc. Am. A 35, 256–261 (2018).
[Crossref]

2017 (1)

S. Kumar and R. Richards-Kortum, “Optical molecular imaging agents for cancer diagnostics and therapeutics,” Nanomedicine 1, 23–30 (2017).
[Crossref]

2016 (8)

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

S. X. Jiang, J. Liu, Y. An, G. L. Zhang, J. Z. Ye, Y. M. Mao, K. S. He, C. W. Chi, and J. Tian, “Novel l2, 1-norm optimization method for fluorescence molecular tomography reconstruction,” Biomed. Opt. Express 7, 2342–2359 (2016).
[Crossref]

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 1: technical principles,” Phys. Med. Biol. 61, 1439–1451 (2016).
[Crossref]

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction,” Phys. Med. Biol. 61, 1452–1475 (2016).
[Crossref]

P. Mohajerani and V. Ntziachristos, “An inversion scheme for hybrid fluorescence molecular tomography using a Fuzzy inference system,” IEEE Trans. Med. Imaging 35, 381–390 (2016).
[Crossref]

W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016).
[Crossref]

A. Savchenko, “Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing,” Knowledge-Based Syst. 91, 252–262 (2016).
[Crossref]

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

2015 (2)

P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
[Crossref]

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

2014 (6)

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

B. Q. Li, F. Maafi, R. Berti, P. Pouliot, E. Rhéaume, J. C. L. Tardif, and F. Lesage, “Hybrid FMT-MRI applied to in vivo atherosclerosis imaging,” Biomed. Opt. Express 5, 1664–1676 (2014).
[Crossref]

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

J. Zhang, J. Shi, X. Cao, F. Liu, J. Bai, and J. Luo, “Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy,” J. Opt. Soc. Am. A 31, 1886–1894 (2014).
[Crossref]

2013 (1)

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

2012 (1)

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

2011 (3)

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Y. Yao, “The superiority of three way decision in probabilistic rough set models,” Inf. Sci. 181, 1080–1096 (2011).
[Crossref]

M. A. Naser and M. S. Patterson, “Improved bioluminescence and fluorescence reconstruction algorithms using diffuse optical tomography, normalized data, and optimized selection of the permissible source region,” Biomed. Opt. Express 2, 169–184 (2011).
[Crossref]

2010 (1)

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

2007 (1)

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

2002 (1)

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[Crossref]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Prob. 15, R41–R93 (1999).
[Crossref]

1995 (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref]

Ale, A.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

An, Y.

Arridge, S.

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction,” Phys. Med. Biol. 61, 1452–1475 (2016).
[Crossref]

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 1: technical principles,” Phys. Med. Biol. 61, 1439–1451 (2016).
[Crossref]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Prob. 15, R41–R93 (1999).
[Crossref]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref]

Bai, J.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

J. Zhang, J. Shi, X. Cao, F. Liu, J. Bai, and J. Luo, “Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy,” J. Opt. Soc. Am. A 31, 1886–1894 (2014).
[Crossref]

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Beer, A. J.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Berti, R.

Braren, R.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Bremer, C.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[Crossref]

Cao, X.

Chen, D.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

Chen, Y.

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Cheng, D. F.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Chi, C. W.

S. X. Jiang, J. Liu, Y. An, G. L. Zhang, J. Z. Ye, Y. M. Mao, K. S. He, C. W. Chi, and J. Tian, “Novel l2, 1-norm optimization method for fluorescence molecular tomography reconstruction,” Biomed. Opt. Express 7, 2342–2359 (2016).
[Crossref]

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Cohrs, C.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

Correia, T.

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction,” Phys. Med. Biol. 61, 1452–1475 (2016).
[Crossref]

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 1: technical principles,” Phys. Med. Biol. 61, 1439–1451 (2016).
[Crossref]

Darne, C.

C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

de Angelis, M. H.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref]

Du, Y.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Ermolayev, V.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

Figueiredo, M.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Freyer, M.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

Guang, H. Z.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

He, K. S.

He, X.

He, X. W.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Herzog, E.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref]

Hou, Y.

Hou, Y. Q.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Huang, Z.

W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016).
[Crossref]

Jia, X.

X. Jia and L. Shang, “Three-way decisions versus two-way decisions on filtering spam email,” in Transactions on Rough Sets XVIII, J. Peters, A. Skowron, T. Li, Y. Yang, J. Yao, and H. Nguyen, eds. (Springer, 2014), pp. 69–91.

Jiang, S. X.

Kalideris, E.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Kanhirodan, R.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

Kou, D. Q.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Kumar, S.

S. Kumar and R. Richards-Kortum, “Optical molecular imaging agents for cancer diagnostics and therapeutics,” Nanomedicine 1, 23–30 (2017).
[Crossref]

Lesage, F.

Li, B.

B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
[Crossref]

Li, B. Q.

Li, L.

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Li, Q.

W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016).
[Crossref]

Li, W.

W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016).
[Crossref]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

Li, X.

B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
[Crossref]

Liang, J.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

Liu, F.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

J. Zhang, J. Shi, X. Cao, F. Liu, J. Bai, and J. Luo, “Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy,” J. Opt. Soc. Am. A 31, 1886–1894 (2014).
[Crossref]

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Liu, J.

Liu, S. Q.

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Liu, X.

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Lu, Y.

C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

Luo, J.

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

J. Zhang, J. Shi, X. Cao, F. Liu, J. Bai, and J. Luo, “Fast reconstruction of fluorescence molecular tomography via a permissible region extraction strategy,” J. Opt. Soc. Am. A 31, 1886–1894 (2014).
[Crossref]

Luo, J. W.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

Ma, W.

B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
[Crossref]

Maafi, F.

Manjappa, R.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

Mao, Y. M.

S. X. Jiang, J. Liu, Y. An, G. L. Zhang, J. Z. Ye, Y. M. Mao, K. S. He, C. W. Chi, and J. Tian, “Novel l2, 1-norm optimization method for fluorescence molecular tomography reconstruction,” Biomed. Opt. Express 7, 2342–2359 (2016).
[Crossref]

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Mohajerani, P.

P. Mohajerani and V. Ntziachristos, “An inversion scheme for hybrid fluorescence molecular tomography using a Fuzzy inference system,” IEEE Trans. Med. Imaging 35, 381–390 (2016).
[Crossref]

P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
[Crossref]

Naser, M. A.

Nowak, R.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Ntziachristos, V.

P. Mohajerani and V. Ntziachristos, “An inversion scheme for hybrid fluorescence molecular tomography using a Fuzzy inference system,” IEEE Trans. Med. Imaging 35, 381–390 (2016).
[Crossref]

P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
[Crossref]

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[Crossref]

Patterson, M. S.

Peng, J.

Peng, J. Y.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Pohle, K.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Pouliot, P.

Prakash, J.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

Qiu, J. D.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Rhéaume, E.

Richards-Kortum, R.

S. Kumar and R. Richards-Kortum, “Optical molecular imaging agents for cancer diagnostics and therapeutics,” Nanomedicine 1, 23–30 (2017).
[Crossref]

Rosenthal, A.

P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
[Crossref]

Sarantopoulos, A.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

Savchenko, A.

A. Savchenko, “Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing,” Knowledge-Based Syst. 91, 252–262 (2016).
[Crossref]

Schmid, R. M.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Schulz, R. B.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref]

Sevick-Muraca, E.

C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

Shan, B. C.

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Shang, L.

X. Jia and L. Shang, “Three-way decisions versus two-way decisions on filtering spam email,” in Transactions on Rough Sets XVIII, J. Peters, A. Skowron, T. Li, Y. Yang, J. Yao, and H. Nguyen, eds. (Springer, 2014), pp. 69–91.

Shaw, C. B.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

Shi, J.

Shi, J. W.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

Siveke, J.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Soehngen, E.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

Sun, B.

B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
[Crossref]

Tardif, J. C. L.

Themelis, G.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Tian, J.

S. X. Jiang, J. Liu, Y. An, G. L. Zhang, J. Z. Ye, Y. M. Mao, K. S. He, C. W. Chi, and J. Tian, “Novel l2, 1-norm optimization method for fluorescence molecular tomography reconstruction,” Biomed. Opt. Express 7, 2342–2359 (2016).
[Crossref]

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

Trajkovic-Arsic, M.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Tung, C. H.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[Crossref]

Tzoumas, S.

P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
[Crossref]

Wang, J. D.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Wang, X.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Wang, X. D.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Wang, Z. L.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Wei, H.

Weissleder, R.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[Crossref]

Wester, J.

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

Wright, S.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Yalavarthy, P. K.

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

Yao, Y.

Y. Yao, “The superiority of three way decision in probabilistic rough set models,” Inf. Sci. 181, 1080–1096 (2011).
[Crossref]

Y. Yao, “Three-way decision: an interpretation of rules in rough set theory,” in International Conference on Rough Sets and Knowledge Technology, P. Wen, Y. Li, L. Polkowski, Y. Yao, S. Tsumoto, and G. Wang, eds. (Springer, 2009), pp. 642–649.

Ye, J.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Ye, J. Z.

Yi, H.

H. Yi, H. Wei, J. Peng, Y. Hou, and X. He, “Adaptive threshold method for recovered FMT,” J. Opt. Soc. Am. A 35, 256–261 (2018).
[Crossref]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

Yi, H. J.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Zhang, B.

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Zhang, G. L.

Zhang, J.

Zhang, J. L.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

Zhang, Q.

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Zhang, X.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Zhang, Y.

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

Zhao, F. J.

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

Zhu, S.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

Zientkowska, M.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

Zuo, S. M.

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

Biomed. Opt. Express (3)

Biomed. Res. Int. (1)

H. J. Yi, X. Zhang, J. Y. Peng, F. J. Zhao, X. D. Wang, Y. Q. Hou, D. F. Cheng, and X. W. He, “Reconstruction for limited-projection fluorescence molecular tomography based on a double-mesh strategy,” Biomed. Res. Int. 2016, 1–11 (2016).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Prakash, C. B. Shaw, R. Manjappa, R. Kanhirodan, and P. K. Yalavarthy, “Sparse recovery methods hold promise for diffuse optical tomographic image reconstruction,” IEEE J. Sel. Top. Quantum Electron. 20, 74–82 (2014).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

IEEE Signal Process. Mag. (1)

P. Mohajerani, S. Tzoumas, A. Rosenthal, and V. Ntziachristos, “Optical and optoacoustic model-based tomography: theory and current challenges for deep tissue imaging of optical contrast,” IEEE Signal Process. Mag. 32(1), 88–100 (2015).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

J. L. Zhang, J. W. Shi, H. Z. Guang, S. M. Zuo, F. Liu, J. Bai, and J. W. Luo, “Iterative correction scheme based on discrete cosine transform and L1 regularization for fluorescence molecular tomography with background fluorescence,” IEEE Trans. Biomed. Eng. 63, 1107–1115 (2016).
[Crossref]

IEEE Trans. Med. Imaging (2)

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[Crossref]

P. Mohajerani and V. Ntziachristos, “An inversion scheme for hybrid fluorescence molecular tomography using a Fuzzy inference system,” IEEE Trans. Med. Imaging 35, 381–390 (2016).
[Crossref]

IEEE Trans. Nucl. Sci. (1)

S. Q. Liu, B. Zhang, X. Wang, L. Li, Y. Chen, X. Liu, F. Liu, B. C. Shan, and J. Bai, “A dual modality system for simultaneous fluorescence and positron emission tomography imaging of small animals,” IEEE Trans. Nucl. Sci. 58, 51–57 (2011).
[Crossref]

Inf. Sci. (1)

Y. Yao, “The superiority of three way decision in probabilistic rough set models,” Inf. Sci. 181, 1080–1096 (2011).
[Crossref]

Int. J. Approx. Reason. (1)

B. Sun, W. Ma, B. Li, and X. Li, “Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set,” Int. J. Approx. Reason. 93, 424–442 (2018).
[Crossref]

Int. J. Nanomed. (1)

Y. Zhang, B. Zhang, F. Liu, J. Luo, and J. Bai, “In vivo tomographic imaging with fluorescence and MRI using tumor-targeted dual-labeled nanoparticles,” Int. J. Nanomed. 9, 33–41 (2014).
[Crossref]

Inverse Prob. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Prob. 15, R41–R93 (1999).
[Crossref]

J. Biomed. Opt. (1)

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of florescence molecular tomography: a comparative study,” J. Biomed. Opt. 18, 467–472 (2013).
[Crossref]

J. Nucl. Med. (1)

M. Trajkovic-Arsic, A. Sarantopoulos, G. Themelis, E. Kalideris, A. J. Beer, K. Pohle, J. Wester, R. M. Schmid, V. Ntziachristos, R. Braren, and J. Siveke, “Molecular imaging of integrin avß3 for in vivo detection of precursor lesions and pancreatic cancer,” J. Nucl. Med. 55, 446–451 (2014).
[Crossref]

J. Opt. Soc. Am. A (2)

Knowledge-Based Syst. (2)

W. Li, Z. Huang, and Q. Li, “Three-way decisions based software defect prediction,” Knowledge-Based Syst. 91, 263–274 (2016).
[Crossref]

A. Savchenko, “Fast multi-class recognition of piecewise regular objects based on sequential three-way decisions and granular computing,” Knowledge-Based Syst. 91, 252–262 (2016).
[Crossref]

Med. Phys. (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref]

Nanomedicine (1)

S. Kumar and R. Richards-Kortum, “Optical molecular imaging agents for cancer diagnostics and therapeutics,” Nanomedicine 1, 23–30 (2017).
[Crossref]

Nat. Med. (1)

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[Crossref]

Nat. Methods (1)

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods 9, 615–620 (2012).
[Crossref]

Phys. Med. Biol. (3)

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 1: technical principles,” Phys. Med. Biol. 61, 1439–1451 (2016).
[Crossref]

T. Correia and S. Arridge, “Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction,” Phys. Med. Biol. 61, 1452–1475 (2016).
[Crossref]

C. Darne, Y. Lu, and E. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms, and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

Sci. Rep. (1)

C. W. Chi, Q. Zhang, Y. M. Mao, D. Q. Kou, J. D. Qiu, J. Ye, J. D. Wang, Z. L. Wang, Y. Du, and J. Tian, “Increased precision of orthotopic and metastatic breast cancer surgery guided by matrix metalloproteinase-activatable near-infrared florescence probes,” Sci. Rep. 5, 562–564 (2015).
[Crossref]

Other (2)

Y. Yao, “Three-way decision: an interpretation of rules in rough set theory,” in International Conference on Rough Sets and Knowledge Technology, P. Wen, Y. Li, L. Polkowski, Y. Yao, S. Tsumoto, and G. Wang, eds. (Springer, 2009), pp. 642–649.

X. Jia and L. Shang, “Three-way decisions versus two-way decisions on filtering spam email,” in Transactions on Rough Sets XVIII, J. Peters, A. Skowron, T. Li, Y. Yang, J. Yao, and H. Nguyen, eds. (Springer, 2014), pp. 69–91.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Flow chart of the reconstruction strategy based on three-way decisions.
Fig. 2.
Fig. 2. Model of single fluorescent target reconstruction, which includes five organs and a target.
Fig. 3.
Fig. 3. First row shows the 2D views (z=15mm) of the reconstructed results by IVTCG with no post-processing, IVTCG+artificial threshold and IVTCG+TWD. Second row shows the 2D views (z=15mm) by CGLS with no post-processing, CGLS+artificial threshold and CGLS+TWD. Third row shows the 2D views (z=15mm) of results by GPSR with no post-processing, GPSR+artificial threshold and GPSR+TWD.
Fig. 4.
Fig. 4. Reconstruction results of IVTCG and IVTCG+TWD methods under different proportions of noise levels. (a) The location errors with different noise levels. (b) The nRMSEs with different noise levels.
Fig. 5.
Fig. 5. (a) Anatomical structure of real mice. (b) Vertical view of the fluorescent target at z=7.4mm.
Fig. 6.
Fig. 6. First row shows the 2D views (x=20.2mm) of the reconstructed results by IVTCG with no post-processing, IVTCG+artificial threshold and IVTCG+TWD. Second row shows the 2D views (x=20.2mm) by CGLS with no post-processing, CGLS+artificial threshold and CGLS+TWD. Third row shows the 2D views (x=20.2mm) of results by GPSR with no post-processing, GPSR+artificial threshold and GPSR+TWD.

Tables (5)

Tables Icon

Table 1. TWD for Fluorescent Target Recognition of FMT

Tables Icon

Table 2. Cost Function Matrix for Fluorescent Target Prediction Based on TWD

Tables Icon

Table 3. Quantitative Analysis of Single Target Reconstruction Results

Tables Icon

Table 4. Quantitative Analysis of the Reconstruction Results of IVTCG+TWD under Different Excitation Points

Tables Icon

Table 5. Quantitative Analysis of Experimental Reconstruction Results of Real Mice

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

{·(Dx(r)ϕx(r))+μax(r)ϕx(r)=Θδ(rrs)·(Dm(r)ϕm(r))+μam(r)ϕm(r)=ϕx(r)ημaf(r)(rΩ),
ϕmmeas=AX,whereX0,
X=argminX0,XΩ{AXϕmmeas22+λXq},
P¯={1if nodei is within the permissible region0otherwise.
X=argminX0,XPR{AXϕmmeas22+λXp},
(P)Ifp(T|t)β,decidetPOS(T);(B)Ifα<p(T|t)<β,decidetBND(T);(N)Ifp(T|t)α,decidetNEG(T).

Metrics