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

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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]

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]

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]

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.

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

Zhang, J. L.

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Zuo, S. M.

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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).
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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).
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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).
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Inverse Prob. (1)

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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=15  mm) of the reconstructed results by IVTCG with no post-processing, IVTCG+artificial threshold and IVTCG+TWD. Second row shows the 2D views (z=15  mm) by CGLS with no post-processing, CGLS+artificial threshold and CGLS+TWD. Third row shows the 2D views (z=15  mm) 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=7.4  mm.
Fig. 6.
Fig. 6. First row shows the 2D views (x=20.2  mm) of the reconstructed results by IVTCG with no post-processing, IVTCG+artificial threshold and IVTCG+TWD. Second row shows the 2D views (x=20.2  mm) by CGLS with no post-processing, CGLS+artificial threshold and CGLS+TWD. Third row shows the 2D views (x=20.2  mm) of results by GPSR with no post-processing, GPSR+artificial threshold and GPSR+TWD.

Tables (5)

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Table 1. TWD for Fluorescent Target Recognition of FMT

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

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Table 3. Quantitative Analysis of Single Target Reconstruction Results

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

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

Equations (6)

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{·(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,where  X0,
X=argminX0,XΩ{AXϕmmeas22+λXq},
P¯={1if node  i is within the permissible region0otherwise.
X=argminX0,XPR{AXϕmmeas22+λXp},
(P)If  p(T|t)β,decide  tPOS(T);(B)If  α<p(T|t)<β,decide  tBND(T);(N)If  p(T|t)α,decide  tNEG(T).

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