Abstract

To measure the activity of tissue at the microscopic level, laminar optical tomography (LOT), which is a microscopic form of diffuse optical tomography, has been developed. However, obtaining sufficient recording speed to determine rapidly changing dynamic activity remains major challenges. For a high frame rate of the reconstructed data, we here propose a new LOT method using compressed sensing theory, called compressive laminar optical tomography (CLOT), in which novel digital micromirror device-based illumination and data reduction in a single reconstruction are applied. In the simulation experiments, the reconstructed volumetric images of the action potentials that were acquired from 5 measured images with random pattern featured a wave border at least to a depth of 2.5 mm. Consequently, it was shown that CLOT has potential for over 200 fps required for the cardiac electrophysiological phenomena.

© 2017 Optical Society of America

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References

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    [Crossref]
  3. Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
    [Crossref]
  4. B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
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    [Crossref]
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    [Crossref]
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2017 (2)

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

2016 (2)

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

X. Yuan and S. Pang, “Structured illumination temporal compressive microscopy,” Biomed. Opt. Express 7(3), 746–758 (2016).
[Crossref] [PubMed]

2015 (2)

D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
[Crossref]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

2014 (2)

O. Berenfeld, M. Yamazaki, D. Filgueiras-Rama, and J. Kalifa, “Surface and intramural reentrant patterns during atrial fibrillation in the sheep,” Methods Inf. Med. 53(4), 314 (2014).
[Crossref] [PubMed]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

2013 (3)

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. Circ. Physiol. 18(5), 050902 (2013).
[Crossref]

E. J. Candés and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2013).
[Crossref]

Y. August, C. Vachman, Y. Rivenson, and A. Stern, “Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains,” Appl. Opt. 52(10), D46–D54 (2013).
[Crossref] [PubMed]

2012 (4)

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
[Crossref] [PubMed]

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
[Crossref]

2011 (1)

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded strobing photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 671–686 (2011).
[Crossref]

2010 (6)

S. A. Burgess, D. Ratner, B. R. Chen, and E. M. C. Hillman, “Fiber-optic and articulating arm implementations of laminar optical tomography for clinical applications,” Biomed. Opt. Express 1(3), 780–790 (2010).
[Crossref]

Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an Optical-Sectioning Compressive Sensing Microscope (CSM),” Opt. Express 18, 24565–24578 (2010).
[Crossref] [PubMed]

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
[Crossref] [PubMed]

M. Süzen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express 18, 23676–23690 (2010).
[Crossref] [PubMed]

J. Ma and G. Plonka, “The curvelet transform,” IEEE Signal Process. Mag. 27(2), 118–133 (2010).
[Crossref]

2009 (4)

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[Crossref] [PubMed]

B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
[Crossref] [PubMed]

E. M. C. Hillman and S. A. Burgess, “Sub-millimeter resolution 3D optical imaging of living tissue using laminar optical tomography,” Laser & Photon. Rev. 3(1–2), 159–179 (2009).
[Crossref]

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

2008 (3)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2008).
[Crossref]

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

2007 (5)

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–120 (2007).
[Crossref]

C. Antzelevitch, “Heterogeneity and cardiac arrhythmias: an overview,” Heart Rhythm 4(7), 964–972 (2007).
[Crossref] [PubMed]

E. M. C. Hillman, O. Bernus, E. Pease, M. B. Bouchard, and A. Pertsov, “Depth-resolved optical imaging of transmural electrical propagation in perfused heart,” Opt. Express 15(26), 17827–17841 (2007).
[Crossref]

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
[Crossref] [PubMed]

Y. M. Lu and M. N. Do, “Multidimensional directional filter banks and surfacelets,” IEEE Trans. Image Process. 16(4), 918–931 (2007).
[Crossref] [PubMed]

2006 (1)

R. H. Clayton, E. A. Zhuchkova, and A. V. Panfilov, “Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation,” Prog. Biophys. Mol. Biol. 90(1), 378–398 (2006).
[Crossref]

2005 (1)

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

2004 (1)

AG. Kléber and Y. Rudy, “Basic mechanisms of cardiac impulse propagation and associated arrhythmias,” Physiol. Rev. 84(2), 431–488 (2004).
[Crossref] [PubMed]

2001 (1)

C. Antzelevitch and J. Fish, “Electrical heterogeneity within the ventricular wall,” Basic Res. Cardiol. 96(6), 517–527 (2001).
[Crossref]

2000 (1)

Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
[Crossref] [PubMed]

Antzelevitch, C.

C. Antzelevitch, “Heterogeneity and cardiac arrhythmias: an overview,” Heart Rhythm 4(7), 964–972 (2007).
[Crossref] [PubMed]

C. Antzelevitch and J. Fish, “Electrical heterogeneity within the ventricular wall,” Basic Res. Cardiol. 96(6), 517–527 (2001).
[Crossref]

Arce, G. R.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an Optical-Sectioning Compressive Sensing Microscope (CSM),” Opt. Express 18, 24565–24578 (2010).
[Crossref] [PubMed]

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

Arthur, R. M.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
[Crossref] [PubMed]

Aster, R. C.

R. C. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, 2 Edition (Academic Press, 2011).

August, Y.

Azimipour, M.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

Bacskai, B. J.

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
[Crossref] [PubMed]

Baher, A.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Baraniuk, R. G.

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–120 (2007).
[Crossref]

Baranluk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Baumgartner, R.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

Berenfeld, O.

O. Berenfeld, M. Yamazaki, D. Filgueiras-Rama, and J. Kalifa, “Surface and intramural reentrant patterns during atrial fibrillation in the sheep,” Methods Inf. Med. 53(4), 314 (2014).
[Crossref] [PubMed]

Bernus, O.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2008).
[Crossref]

Blackwell, T. R.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Boas, D. A.

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[Crossref] [PubMed]

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
[Crossref] [PubMed]

D. A. Boas, C. Pitris, and N. Ramanujam, Handbook of Biomedical Optics (CRC Press, 2011), pp. 92.

Bobin, J.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
[Crossref]

Borchers, B.

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B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
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E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
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E. M. C. Hillman, O. Bernus, E. Pease, M. B. Bouchard, and A. Pertsov, “Depth-resolved optical imaging of transmural electrical propagation in perfused heart,” Opt. Express 15(26), 17827–17841 (2007).
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G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
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Burgess, S. A.

S. A. Burgess, D. Ratner, B. R. Chen, and E. M. C. Hillman, “Fiber-optic and articulating arm implementations of laminar optical tomography for clinical applications,” Biomed. Opt. Express 1(3), 780–790 (2010).
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E. M. C. Hillman and S. A. Burgess, “Sub-millimeter resolution 3D optical imaging of living tissue using laminar optical tomography,” Laser & Photon. Rev. 3(1–2), 159–179 (2009).
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B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
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V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
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Chen, C.

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
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Chen, P.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
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Chen, Y.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
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M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
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Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

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F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
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D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
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M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
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Dahan, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
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Dale, A. M.

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
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M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
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Devor, A.

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
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Dhamne, S.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
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Y. M. Lu and M. N. Do, “Multidimensional directional filter banks and surfacelets,” IEEE Trans. Image Process. 16(4), 918–931 (2007).
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M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
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M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
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Dunn, A. K.

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
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Durduran, T.

Efimov, I. R.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
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J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
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Eldar, Y. C.

Y. C. Eldar and G. Kutyniok, Compressed Sensing Theory and Applications (Cambridge, 2012).
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Elnatan, D.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

Erzurumlu, R. S.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

Fang, Q.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2008).
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Filgueiras-Rama, D.

O. Berenfeld, M. Yamazaki, D. Filgueiras-Rama, and J. Kalifa, “Surface and intramural reentrant patterns during atrial fibrillation in the sheep,” Methods Inf. Med. 53(4), 314 (2014).
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M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
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Garfinkel, A.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
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Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
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Giannoula, A.

Glavin, M.

D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
[Crossref]

Glunde, K.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Helmstetter, F. J.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

Hillman, E. M.

B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
[Crossref] [PubMed]

Hillman, E. M. C.

S. A. Burgess, D. Ratner, B. R. Chen, and E. M. C. Hillman, “Fiber-optic and articulating arm implementations of laminar optical tomography for clinical applications,” Biomed. Opt. Express 1(3), 780–790 (2010).
[Crossref]

E. M. C. Hillman and S. A. Burgess, “Sub-millimeter resolution 3D optical imaging of living tissue using laminar optical tomography,” Laser & Photon. Rev. 3(1–2), 159–179 (2009).
[Crossref]

E. M. C. Hillman, O. Bernus, E. Pease, M. B. Bouchard, and A. Pertsov, “Depth-resolved optical imaging of transmural electrical propagation in perfused heart,” Opt. Express 15(26), 17827–17841 (2007).
[Crossref]

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
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A. K. Iranmahboob and E. M. C. Hillman, “Diffusion vs. Monte Carlo for Image Reconstruction in Mesoscopic Volumes,” OSA Biomedical Topical Meetings, OSA Technical Digest (2008).

Huang, B.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

Intes, X.

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

Iranmahboob, A.

B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
[Crossref] [PubMed]

Iranmahboob, A. K.

A. K. Iranmahboob and E. M. C. Hillman, “Diffusion vs. Monte Carlo for Image Reconstruction in Mesoscopic Volumes,” OSA Biomedical Topical Meetings, OSA Technical Digest (2008).

Ji, R.

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

Jones, E.

D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
[Crossref]

Kalifa, J.

O. Berenfeld, M. Yamazaki, D. Filgueiras-Rama, and J. Kalifa, “Surface and intramural reentrant patterns during atrial fibrillation in the sheep,” Methods Inf. Med. 53(4), 314 (2014).
[Crossref] [PubMed]

Karma, A.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Kil, J.

Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
[Crossref] [PubMed]

Kilmartin, L.

D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
[Crossref]

Kittle, D. S.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
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AG. Kléber and Y. Rudy, “Basic mechanisms of cardiac impulse propagation and associated arrhythmias,” Physiol. Rev. 84(2), 431–488 (2004).
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Krauss, G.W.

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
[Crossref] [PubMed]

Kutyniok, G.

Y. C. Eldar and G. Kutyniok, Compressed Sensing Theory and Applications (Cambridge, 2012).
[Crossref]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Laughner, J. I.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
[Crossref] [PubMed]

Lehrer, N.

B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
[Crossref] [PubMed]

Li, Q.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Lin, J.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

Lin, Z. J.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
[Crossref] [PubMed]

Liu, H.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
[Crossref] [PubMed]

Liu, Q.

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. Circ. Physiol. 18(5), 050902 (2013).
[Crossref]

Liu, Y.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

Lu, Y. M.

Y. M. Lu and M. N. Do, “Multidimensional directional filter banks and surfacelets,” IEEE Trans. Image Process. 16(4), 918–931 (2007).
[Crossref] [PubMed]

Ma, J.

J. Ma and G. Plonka, “The curvelet transform,” IEEE Signal Process. Mag. 27(2), 118–133 (2010).
[Crossref]

Mahajan, A.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

McGinley, B.

D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
[Crossref]

Mirza, I. O.

Mousavi, H. S.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
[Crossref]

Naphas, R.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Ng, F. S.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
[Crossref] [PubMed]

Nguyen, B. B.

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

Niu, H.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
[Crossref] [PubMed]

Olcese, R.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Ozturk, M. S.

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

Panfilov, A. V.

R. H. Clayton, E. A. Zhuchkova, and A. V. Panfilov, “Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation,” Prog. Biophys. Mol. Biol. 90(1), 378–398 (2006).
[Crossref]

Pang, S.

Paredes, J. L.

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

Pashaie, R.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

Pease, E.

Pertsov, A.

Pitris, C.

D. A. Boas, C. Pitris, and N. Ramanujam, Handbook of Biomedical Optics (CRC Press, 2011), pp. 92.

Plonka, G.

J. Ma and G. Plonka, “The curvelet transform,” IEEE Signal Process. Mag. 27(2), 118–133 (2010).
[Crossref]

Prather, D. W.

Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an Optical-Sectioning Compressive Sensing Microscope (CSM),” Opt. Express 18, 24565–24578 (2010).
[Crossref] [PubMed]

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

Qu, Z.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
[Crossref] [PubMed]

Raman, V.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Ramanujam, N.

D. A. Boas, C. Pitris, and N. Ramanujam, Handbook of Biomedical Optics (CRC Press, 2011), pp. 92.

Raskar, R.

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded strobing photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 671–686 (2011).
[Crossref]

Ratner, D.

Reddy, D.

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded strobing photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 671–686 (2011).
[Crossref]

Restrepo, J. G.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Rivenson, Y.

Rudy, Y.

AG. Kléber and Y. Rudy, “Basic mechanisms of cardiac impulse propagation and associated arrhythmias,” Physiol. Rev. 84(2), 431–488 (2004).
[Crossref] [PubMed]

Sato, D.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Sheikhzadeh, M.

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

Shiferaw, Y.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Skoch, J.

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
[Crossref] [PubMed]

Stern, A.

Studer, V.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
[Crossref]

Sulkin, M. S.

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
[Crossref] [PubMed]

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Süzen, M.

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

Tang, Q.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

Thurber, C. H.

R. C. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, 2 Edition (Academic Press, 2011).

Tian, F.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
[Crossref] [PubMed]

Tsytsarev, V.

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

Vachman, C.

Veeraraghavan, A.

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded strobing photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 671–686 (2011).
[Crossref]

Vetterli, M.

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

Wakin, M. B.

E. J. Candés and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2013).
[Crossref]

Wang, G.

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

Weiss, J. N.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
[Crossref] [PubMed]

Wierwille, J.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Winnard, P. T.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Wu, Y.

Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an Optical-Sectioning Compressive Sensing Microscope (CSM),” Opt. Express 18, 24565–24578 (2010).
[Crossref] [PubMed]

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

Xie, F.

Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
[Crossref] [PubMed]

Xie, L.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Yamazaki, M.

O. Berenfeld, M. Yamazaki, D. Filgueiras-Rama, and J. Kalifa, “Surface and intramural reentrant patterns during atrial fibrillation in the sheep,” Methods Inf. Med. 53(4), 314 (2014).
[Crossref] [PubMed]

Yang, F.

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

Yang, M.

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Ye, P.

Y. Wu, P. Ye, I. O. Mirza, G. R. Arce, and D. W. Prather, “Experimental demonstration of an Optical-Sectioning Compressive Sensing Microscope (CSM),” Opt. Express 18, 24565–24578 (2010).
[Crossref] [PubMed]

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

Yuan, B.

B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
[Crossref] [PubMed]

Yuan, S.

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

Yuan, X.

Zhang, W.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

Zhao, L.

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

Zhu, C.

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. Circ. Physiol. 18(5), 050902 (2013).
[Crossref]

Zhu, L.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

Zhuchkova, E. A.

R. H. Clayton, E. A. Zhuchkova, and A. V. Panfilov, “Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation,” Prog. Biophys. Mol. Biol. 90(1), 378–398 (2006).
[Crossref]

Am. J. Physiol. Heart. Circ. Physiol. (2)

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303(7), H753–H765 (2012).
[Crossref] [PubMed]

J. I. Laughner, F. S. Ng, M. S. Sulkin, R. M. Arthur, and I. R. Efimov, “Processing and analysis of cardiac optical mapping data obtained with potentiometric dyes,” Am. J. Physiol. Heart. Circ. Physiol. 303, H753–H765 (2012).
[Crossref] [PubMed]

Ann. Biomed. Eng. (1)

M. S. Ozturk, C. Chen, R. Ji, L. Zhao, B. B. Nguyen, J. P. Fisher, Y. Chen, and X. Intes, “Mesoscopic Fluorescence Molecular Tomography for Evaluating Engineered Tissues,” Ann. Biomed. Eng. 44(3), 667–679 (2016).
[Crossref]

Appl. Opt. (1)

Basic Res. Cardiol. (1)

C. Antzelevitch and J. Fish, “Electrical heterogeneity within the ventricular wall,” Basic Res. Cardiol. 96(6), 517–527 (2001).
[Crossref]

Biomed. Opt. Express (2)

Biophys. J. (2)

Z. Qu, J. Kil, F. Xie, A. Garfinkel, and J. N. Weiss, “Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation,” Biophys. J. 78(6), 2761–2775 (2000).
[Crossref] [PubMed]

A. Mahajan, Y. Shiferaw, D. Sato, A. Baher, R. Olcese, L. Xie, M. Yang, P. Chen, J. G. Restrepo, A. Karma, A. Garfinkel, Z. Qu, and J. N. Weiss, “A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates,” Biophys. J. 94(2), 392–410 (2008).
[Crossref]

Heart Rhythm (1)

C. Antzelevitch, “Heterogeneity and cardiac arrhythmias: an overview,” Heart Rhythm 4(7), 964–972 (2007).
[Crossref] [PubMed]

IEEE J. Biomed. Health Inform. (1)

D. Craven, B. McGinley, L. Kilmartin, M. Glavin, and E. Jones, “Compressed sensing for bioelectric signals: a review,” IEEE J. Biomed. Health Inform. 19(2), 529–540 (2015).
[Crossref]

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

Y. Chen, S. Yuan, J. Wierwille, R. Naphas, Q. Li, T. R. Blackwell, P. T. Winnard, V. Raman, and K. Glunde, “Integrated optical coherence tomography (OCT) and fluorescence laminar optical tomography (FLOT),” IEEE J. Sel. Topics Quantum Electron. 16(4), 755–766 (2010).
[Crossref]

IEEE Signal Process. Mag. (5)

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Signal Process. Mag. 31(1), 105–115 (2014).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baranluk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83 (2008).
[Crossref]

R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–120 (2007).
[Crossref]

E. J. Candés and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2013).
[Crossref]

J. Ma and G. Plonka, “The curvelet transform,” IEEE Signal Process. Mag. 27(2), 118–133 (2010).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

F. Yang, M. S. Ozturk, L. Zhao, W. Cong, G. Wang, and X. Intes, “High-resolution mesoscopic fluorescence molecular tomography based on compressive sensing,” IEEE Trans. Biomed. Eng. 62(1), 248–255 (2015).
[Crossref]

IEEE Trans. Image Process. (3)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2008).
[Crossref]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14(12), 2091–2106 (2005).
[Crossref] [PubMed]

Y. M. Lu and M. N. Do, “Multidimensional directional filter banks and surfacelets,” IEEE Trans. Image Process. 16(4), 918–931 (2007).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

A. Veeraraghavan, D. Reddy, and R. Raskar, “Coded strobing photography: Compressive sensing of high speed periodic videos,” IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 671–686 (2011).
[Crossref]

J. Biomed Opt. (2)

M. Azimipour, M. Sheikhzadeh, R. Baumgartner, P. K. Cullen, F. J. Helmstetter, W. Chang, and R. Pashaie, “Fluorescence laminar optical tomography for brain imaging: system implementation and performance evaluation,” J. Biomed Opt. 22(1), 016003 (2017).
[Crossref]

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed Opt. 15, 046005 (2010).
[Crossref] [PubMed]

J. Biomed. Opt. Circ. Physiol. (1)

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. Circ. Physiol. 18(5), 050902 (2013).
[Crossref]

Laser & Photon. Rev. (1)

E. M. C. Hillman and S. A. Burgess, “Sub-millimeter resolution 3D optical imaging of living tissue using laminar optical tomography,” Laser & Photon. Rev. 3(1–2), 159–179 (2009).
[Crossref]

Methods Inf. Med. (1)

O. Berenfeld, M. Yamazaki, D. Filgueiras-Rama, and J. Kalifa, “Surface and intramural reentrant patterns during atrial fibrillation in the sheep,” Methods Inf. Med. 53(4), 314 (2014).
[Crossref] [PubMed]

Nat Methods (1)

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

Neuroimage (1)

E. M. C. Hillman, A. Devor, M. B. Bouchard, A. K. Dunn, G.W. Krauss, J. Skoch, B. J. Bacskai, A. M. Dale, and D. A. Boas, “Depth-resolved optical imaging and microscopy of vascular compartment dynamics during somatosensory stimulation,” Neuroimage 35(1), 89–104 (2007).
[Crossref] [PubMed]

Neurophotonics. (1)

Q. Tang, J. Lin, V. Tsytsarev, R. S. Erzurumlu, Y. Liu, and Y. Chen, “Review of mesoscopic optical tomography for depth-resolved imaging of hemodynamic changes and neural activities,” Neurophotonics. 4(1), 011009 (2017).
[Crossref]

Opt. Express (4)

Physiol. Rev. (1)

AG. Kléber and Y. Rudy, “Basic mechanisms of cardiac impulse propagation and associated arrhythmias,” Physiol. Rev. 84(2), 431–488 (2004).
[Crossref] [PubMed]

Proc Natl Acad Sci USA (1)

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc Natl Acad Sci USA 109(26), 1679–1687 (2012).
[Crossref]

Proc. SPIE (1)

P. Ye, J. L. Paredes, Y. Wu, C. Chen, G. R. Arce, and D. W. Prather, “Compressive confocal microscopy: 3D reconstruction algorithms,” Proc. SPIE 7210, 72100G (2009).
[Crossref]

Prog. Biophys. Mol. Biol. (1)

R. H. Clayton, E. A. Zhuchkova, and A. V. Panfilov, “Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation,” Prog. Biophys. Mol. Biol. 90(1), 378–398 (2006).
[Crossref]

Rev. Sci. Instrum. (1)

B. Yuan, S. A. Burgess, A. Iranmahboob, M. B. Bouchard, N. Lehrer, C. Bordier, and E. M. Hillman, “A system for high-resolution depth-resolved optical imaging of fluorescence and absorption contrast,” Rev. Sci. Instrum. 80(4), 043706 (2009).
[Crossref] [PubMed]

Other (6)

Q. Tang, V. Tsytsarev, J. Lin, Y. Liu, C. Chen, R. S. Erzurumlu, and Y. Chen, “3D mesoscopic imaging of neural connections in sensory and motor cortices,” in Proc. Int. Photon. Conf. 2016 IEEE. ME 4.5 (2016).

A. K. Iranmahboob and E. M. C. Hillman, “Diffusion vs. Monte Carlo for Image Reconstruction in Mesoscopic Volumes,” OSA Biomedical Topical Meetings, OSA Technical Digest (2008).

Y. C. Eldar and G. Kutyniok, Compressed Sensing Theory and Applications (Cambridge, 2012).
[Crossref]

E. J. Candés, “Compressive sampling,” in Proc. Int. Congr. Math.3, 1433–1452 (2006).

D. A. Boas, C. Pitris, and N. Ramanujam, Handbook of Biomedical Optics (CRC Press, 2011), pp. 92.

R. C. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, 2 Edition (Academic Press, 2011).

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Figures (12)

Fig. 1
Fig. 1 Schematic diagram of optical system
Fig. 2
Fig. 2 3D object models
Fig. 3
Fig. 3 Reconstruction error in each model using 10 measurements. Purple *, brown +, and green ▵ indicate the results of DCT, Haar 1.3, and Haar 3.3.
Fig. 4
Fig. 4 Reconstruction error in each model at each depth layer (DCT using 400 irradiation points).
Fig. 5
Fig. 5 Reconstruction error at each depth. (a) in the conventional method with all models, (b) proposed method with 20 measurements (Horizontal 1–3, and Sphere).
Fig. 6
Fig. 6 Reconstructed slice images in Horizontal 3 using 400 irradiation points. The layers in the xy plane are arranged from left to right in order of increasing depth. a: 3D object model, b: slice images of the object model, c: 3D reconstructed data of f by DCT, d: slice images reconstructed from 5 measurement by DCT, e: from 10 measurements by DCT, f: from 20 measurements by DCT, g: 3D reconstructed data of j by Haar 1.3, h: slice images reconstructed from 5 measurement by Haar 1.3, i: from 10 measurements by Haar 3.3, j: from 20 measurements by Haar 1.3, k: 3D reconstructed data of n by Haar 3.3, l: slice images reconstructed from 5 measurement by Haar 3.3, m: from 10 measurements by Haar 3.3, n: from 20 measurements by Haar 3.3.
Fig. 7
Fig. 7 Reconstructed slice images in Sphere using 400 irradiation points. The layers in the xy plane are arranged from left to right in order of increasing depth. a: 3D object model, b: slice images of the object model, c: 3D reconstructed data of f by DCT, d: slice images reconstructed from 5 measurement by DCT, e: from 10 measurements by DCT, f: from 20 measurements by DCT, g: 3D reconstructed data of j by Haar 1.3, h: slice images reconstructed from 5 measurement by Haar 1.3, i: from 10 measurements by Haar 3.3, j: from 20 measurements by Haar 1.3, k: 3D reconstructed data of n by Haar 3.3, l: slice images reconstructed from 5 measurement by Haar 3.3, m: from 10 measurements by Haar 3.3, n: from 20 measurements by Haar 3.3.
Fig. 8
Fig. 8 Reconstruction error stacked bar graph at each depth. A: from 20 measurements at different noise levels. B: by Haar 1.3 with 10% noise.
Fig. 9
Fig. 9 Reconstructed slice images in Horizontal 3 and Sphere with 10% noise. The layers in the xy plane are arranged from left to right in order of increasing depth. a: Horizontal 3 reconstructed by conventional method, b: Sphere reconstructed by conventional method, c: Horizontal 3 reconstructed from 20 measurements using 400 points by DCT, d: Sphere reconstructed from 20 measurements using 400 points by DCT, e: Horizontal 3 reconstructed from 20 measurements using 400 points by Haar 1.3, f: Sphere reconstructed from 20 measurements using 400 points by Haar 1.3, g: Horizontal 3 reconstructed from 20 measurements using 400 points by Haar 3.3, h: Sphere reconstructed from 20 measurements using 400 points by Haar 3.3
Fig. 10
Fig. 10 Reconstructed slice images in Horizontal 3 and Sphere with 30% noise. The layers in the xy plane are arranged from left to right in order of increasing depth. a: Horizontal 3 reconstructed by conventional method, b: Sphere reconstructed by conventional method, c: Horizontal 3 reconstructed from 20 measurements using 400 points by DCT, d: Sphere reconstructed from 20 measurements using 400 points by DCT, e: Horizontal 3 reconstructed from 20 measurements using 400 points by Haar 1.3, f: Sphere reconstructed from 20 measurements using 400 points by Haar 1.3, g: Horizontal 3 reconstructed from 20 measurements using 400 points by Haar 3.3, h: Sphere reconstructed from 20 measurements using 400 points by Haar 3.3
Fig. 11
Fig. 11 Normalized intensity of the sensitivity matrix at each depth.
Fig. 12
Fig. 12 Required number of measurements per second for the frame rate of the reconstructed data (32×32 pixel ROI).

Tables (2)

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Table 1 Number of nonzero entries in DWT. Standard deviations are in parentheses.

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Table 2 Energy of 50 coefficients in descending order in DWT. Standard deviations are in parentheses.

Equations (13)

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P k ( u , v ) = | h e x ( u , v ) * | M o | u k ( M o u , M o v ) | 2
A k ( u , v , t ) = P k ( u , v ) O ( u , v , t )
= ( x , y , z , t ) c ( x , y , z ) τ ( x , y , z , t ) H ( x , y , z ) E ( u x , v y , z ) d x d y d z
I k ( n , m , t ) = | h e m ( n , m ) | 2 * | A k ( n / M d , m / M d , t ) / | M d | | 2
f k ( a , b , t ) = d n d m I k ( n , m , t ) rect ( a n Δ det , b m Δ det ) + ρ a b
Δ F = J Δ V + ρ
y = Φ x
argmin x 1 subject t o y = Φ x
F = J V = J Ψ α
W = [ w w w ]
w = [ c 1 c 2 , , c N ]
c j = 1 max 1 i M a i j
F = J W Ψ α

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