Abstract

Photonics based imaging is a widely utilised technique for the study of biological functions within pre-clinical studies. Specifically, bioluminescence imaging is a sensitive non-invasive and non-contact optical imaging technique that is able to detect distributed (biologically informative) visible and near-infrared activated light sources within tissue, providing information about tissue function. Compressive sensing (CS) is a method of signal processing that works on the basis that a signal or image can be compressed without important information being lost. This work describes the development of a CS based hyperspectral Bioluminescence imaging system that is used to collect compressed fluence data from the external surface of an animal model, due to an internal source, providing lower acquisition times, higher spectral content and potentially better tomographic source localisation. The work demonstrates that hyperspectral surface fluence images of both block and mouse shaped phantom due to internal light sources could be obtained at 30% of the time and measurements it would take to collect the data using conventional raster scanning methods. Using hyperspectral data, tomographic reconstruction of internal light sources can be carried out using any desired number of wavelengths and spectral bandwidth. Reconstructed images of internal light sources using four wavelengths as obtained through CS are presented showing a localisation error of ∼3 mm. Additionally, tomographic images of dual-colored sources demonstrating multi-wavelength light sources being recovered are presented further highlighting the benefits of the hyperspectral system for utilising multi-colored biomarker applications.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2018 (3)

2017 (2)

2016 (1)

2015 (1)

S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
[Crossref]

2013 (4)

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Quantitative surface radiance mapping using multiview images of light-emitting turbid media,” J. Opt. Soc. Am. A 30(12), 2572–2584 (2013).
[Crossref]

J. A. Guggenheim, H. R. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24(10), 105405 (2013).
[Crossref]

M. Cheraghchi, V. Guruswami, and A. Velingker, “Restricted isometry of Fourier matrices and list decodability of random linear codes,” SIAM J. Comput. 42(5), 1888–1914 (2013).
[Crossref]

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput Optim Appl 56(3), 507–530 (2013).
[Crossref]

2012 (1)

2011 (1)

S. Becker, J. Bobin, and E. J. Candès, “NESTA: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4(1), 1–39 (2011).
[Crossref]

2009 (2)

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).
[Crossref]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

2008 (3)

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes rendus mathematique 346(9–10), 589–592 (2008).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
[Crossref]

2007 (3)

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
[Crossref]

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[Crossref]

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[Crossref]

2006 (3)

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
[Crossref]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[Crossref]

2001 (1)

Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy minimization via graph cuts,” IEEE Trans. Pattern Anal. Machine Intell. 23(11), 1222–1239 (2001).
[Crossref]

1998 (1)

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. on Image Process. 7(3), 370–375 (1998).
[Crossref]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60(1–4), 259–268 (1992).
[Crossref]

1976 (1)

1969 (1)

M. R. Hestenes, “Multiplier and gradient methods,” J Optim Theory Appl 4(5), 303–320 (1969).
[Crossref]

1955 (1)

D. W. Peaceman, J. Rachford, and H. Henry, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

Arridge, S.

Baker, C. H.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[Crossref]

Bargigia, I.

Basevi, H. R.

Bassi, A.

Becker, S.

S. Becker, J. Bobin, and E. J. Candès, “NESTA: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4(1), 1–39 (2011).
[Crossref]

Beijnen, J.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
[Crossref]

Betcke, M.

Bobin, J.

S. Becker, J. Bobin, and E. J. Candès, “NESTA: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4(1), 1–39 (2011).
[Crossref]

Boogerd, W.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
[Crossref]

Boykov, Y.

Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy minimization via graph cuts,” IEEE Trans. Pattern Anal. Machine Intell. 23(11), 1222–1239 (2001).
[Crossref]

Bruckstein, A. M.

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).
[Crossref]

Buckle, T.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
[Crossref]

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
[Crossref]

Candes, E.

E. Candes and J. Romberg, “l1-magic: Recovery of sparse signals via convex programming,” URL: www.acm.caltech.edu/l1magic/downloads/l1magic.pdf 4, 14 (2005).

Candes, E. J.

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes rendus mathematique 346(9–10), 589–592 (2008).
[Crossref]

Candès, E. J.

S. Becker, J. Bobin, and E. J. Candès, “NESTA: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4(1), 1–39 (2011).
[Crossref]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

Carter, B. S.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

Carvalho-Gaspar, M.

S. Taylor, J. Guggenheim, I. Styles, M. Carvalho-Gaspar, M. Cobbold, and H. Dehghani, “Importance of free space modelling on quantitative non-contact imaging,” in Biomedical Optics, (Optical Society of America, 2014), BM3A. 46.

Chan, T. F.

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. on Image Process. 7(3), 370–375 (1998).
[Crossref]

Cheraghchi, M.

M. Cheraghchi, V. Guruswami, and A. Velingker, “Restricted isometry of Fourier matrices and list decodability of random linear codes,” SIAM J. Comput. 42(5), 1888–1914 (2013).
[Crossref]

Cobbold, M.

S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
[Crossref]

S. Taylor, J. Guggenheim, I. Styles, M. Carvalho-Gaspar, M. Cobbold, and H. Dehghani, “Importance of free space modelling on quantitative non-contact imaging,” in Biomedical Optics, (Optical Society of America, 2014), BM3A. 46.

Coquoz, O.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[Crossref]

D’andrea, C.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” preprint 93, 2 (2011).

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
[Crossref]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[Crossref]

Dehghani, H.

H. Dehghani, J. A. Guggenheim, S. L. Taylor, X. Xu, and K. K.-H. Wang, “Quantitative bioluminescence tomography using spectral derivative data,” Biomed. Opt. Express 9(9), 4163–4174 (2018).
[Crossref]

J. A. Guggenheim, I. Bargigia, A. Farina, A. Pifferi, and H. Dehghani, “Time resolved diffuse optical spectroscopy with geometrically accurate models for bulk parameter recovery,” Biomed. Opt. Express 7(9), 3784–3794 (2016).
[Crossref]

S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
[Crossref]

J. A. Guggenheim, H. R. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24(10), 105405 (2013).
[Crossref]

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Quantitative surface radiance mapping using multiview images of light-emitting turbid media,” J. Opt. Soc. Am. A 30(12), 2572–2584 (2013).
[Crossref]

H. R. Basevi, K. M. Tichauer, F. Leblond, H. Dehghani, J. A. Guggenheim, R. W. Holt, and I. B. Styles, “Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise,” Biomed. Opt. Express 3(9), 2131–2141 (2012).
[Crossref]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
[Crossref]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[Crossref]

S. Taylor, J. Guggenheim, I. Styles, M. Carvalho-Gaspar, M. Cobbold, and H. Dehghani, “Importance of free space modelling on quantitative non-contact imaging,” in Biomedical Optics, (Optical Society of America, 2014), BM3A. 46.

Di Sieno, L.

Donoho, D.

D. Donoho, “For Most Large Undetennined Systems of Linear Equations the Minimal 11-norm Solution is also the Sparsest Solution,” Technical Report (2004).

Donoho, D. L.

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).
[Crossref]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” preprint 93, 2 (2011).

Ducros, N.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

Edgar, M. P.

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A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).
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M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” preprint 93, 2 (2011).

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Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60(1–4), 259–268 (1992).
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Frampton, J.

J. A. Guggenheim, H. R. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24(10), 105405 (2013).
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J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Quantitative surface radiance mapping using multiview images of light-emitting turbid media,” J. Opt. Soc. Am. A 30(12), 2572–2584 (2013).
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Gibson, G. M.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics, 1 (2018).
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Glinton, S. L.

S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
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S. Taylor, J. Guggenheim, I. Styles, M. Carvalho-Gaspar, M. Cobbold, and H. Dehghani, “Importance of free space modelling on quantitative non-contact imaging,” in Biomedical Optics, (Optical Society of America, 2014), BM3A. 46.

Guggenheim, J. A.

Guruswami, V.

M. Cheraghchi, V. Guruswami, and A. Velingker, “Restricted isometry of Fourier matrices and list decodability of random linear codes,” SIAM J. Comput. 42(5), 1888–1914 (2013).
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Heerschap, A.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
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Henry, H.

D. W. Peaceman, J. Rachford, and H. Henry, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

Hestenes, M. R.

M. R. Hestenes, “Multiplier and gradient methods,” J Optim Theory Appl 4(5), 303–320 (1969).
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Holt, R. W.

Intes, X.

M. Ochoa, Q. Pian, R. Yao, N. Ducros, and X. Intes, “Assessing patterns for compressive fluorescence lifetime imaging,” Opt. Lett. 43(18), 4370–4373 (2018).
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Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
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Jiang, H.

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput Optim Appl 56(3), 507–530 (2013).
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Jiang, S.

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
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Kemper, E.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
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Kiryu, S.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
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Klerk, C. P.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
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Kung, A. L.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
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Kuo, C.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
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Küsters, B.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
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Kutyniok, G.

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” preprint 93, 2 (2011).

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
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Leblond, F.

Leenders, W.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
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Li, C.

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput Optim Appl 56(3), 507–530 (2013).
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Lin, N.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
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Lyons, S.

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
[Crossref]

Mason, S. K.

S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
[Crossref]

Mulligan, R. C.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
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Niers, T. M.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
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Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60(1–4), 259–268 (1992).
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Overmeer, R. M.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
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M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics, 1 (2018).
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Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
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H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
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D. W. Peaceman, J. Rachford, and H. Henry, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
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Pian, Q.

M. Ochoa, Q. Pian, R. Yao, N. Ducros, and X. Intes, “Assessing patterns for compressive fluorescence lifetime imaging,” Opt. Lett. 43(18), 4370–4373 (2018).
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Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
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Pifferi, A.

Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
[Crossref]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
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M. J. Powell, “A method for nonlinear constraints in minimization problems,” Optimization, 283–298 (1969).

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D. W. Peaceman, J. Rachford, and H. Henry, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
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Rice, B. W.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
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Richel, D. J.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
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E. Candes and J. Romberg, “l1-magic: Recovery of sparse signals via convex programming,” URL: www.acm.caltech.edu/l1magic/downloads/l1magic.pdf 4, 14 (2005).

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Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60(1–4), 259–268 (1992).
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Sinsuebphon, N.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
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Sloane, N. J.

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
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Styles, I.

S. Taylor, J. Guggenheim, I. Styles, M. Carvalho-Gaspar, M. Cobbold, and H. Dehghani, “Importance of free space modelling on quantitative non-contact imaging,” in Biomedical Optics, (Optical Society of America, 2014), BM3A. 46.

Styles, I. B.

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
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Szentirmai, O.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

Szucs, S.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

Takahashi, M.

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
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Taylor, S.

S. Taylor, J. Guggenheim, I. Styles, M. Carvalho-Gaspar, M. Cobbold, and H. Dehghani, “Importance of free space modelling on quantitative non-contact imaging,” in Biomedical Optics, (Optical Society of America, 2014), BM3A. 46.

Taylor, S. L.

H. Dehghani, J. A. Guggenheim, S. L. Taylor, X. Xu, and K. K.-H. Wang, “Quantitative bioluminescence tomography using spectral derivative data,” Biomed. Opt. Express 9(9), 4163–4174 (2018).
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S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
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Tichauer, K. M.

Troy, T. L.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
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Valentini, G.

Van Noorden, C. J.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
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van Tellingen, O.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
[Crossref]

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
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Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy minimization via graph cuts,” IEEE Trans. Pattern Anal. Machine Intell. 23(11), 1222–1239 (2001).
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Velingker, A.

M. Cheraghchi, V. Guruswami, and A. Velingker, “Restricted isometry of Fourier matrices and list decodability of random linear codes,” SIAM J. Comput. 42(5), 1888–1914 (2013).
[Crossref]

Versteeg, H. H.

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
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Wang, K. K.-H.

Wong, C.-K.

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. on Image Process. 7(3), 370–375 (1998).
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Xu, H.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[Crossref]

Xu, X.

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

Yao, R.

M. Ochoa, Q. Pian, R. Yao, N. Ducros, and X. Intes, “Assessing patterns for compressive fluorescence lifetime imaging,” Opt. Lett. 43(18), 4370–4373 (2018).
[Crossref]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

Yin, W.

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput Optim Appl 56(3), 507–530 (2013).
[Crossref]

Zabih, R.

Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy minimization via graph cuts,” IEEE Trans. Pattern Anal. Machine Intell. 23(11), 1222–1239 (2001).
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Zhang, Y.

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput Optim Appl 56(3), 507–530 (2013).
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Appl. Opt. (1)

Biomed. Opt. Express (3)

Biotechniques (1)

C. P. Klerk, R. M. Overmeer, T. M. Niers, H. H. Versteeg, D. J. Richel, T. Buckle, C. J. Van Noorden, and O. van Tellingen, “Validity of bioluminescence measurements for noninvasive in vivo imaging of tumor load in small animals,” Biotechniques 43(1S), S7–S13 (2007).
[Crossref]

Commun. Numer. Meth. Engng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

Comptes rendus mathematique (1)

E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” Comptes rendus mathematique 346(9–10), 589–592 (2008).
[Crossref]

Comput Optim Appl (1)

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput Optim Appl 56(3), 507–530 (2013).
[Crossref]

Eur. J. Cancer (1)

E. Kemper, W. Leenders, B. Küsters, S. Lyons, T. Buckle, A. Heerschap, W. Boogerd, J. Beijnen, and O. Van Tellingen, “Development of luciferase tagged brain tumour models in mice for chemotherapy intervention studies,” Eur. J. Cancer 42(18), 3294–3303 (2006).
[Crossref]

IEEE Signal Process. Mag. (2)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[Crossref]

IEEE Trans. on Image Process. (1)

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. on Image Process. 7(3), 370–375 (1998).
[Crossref]

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

Y. Boykov, O. Veksler, and R. Zabih, “Fast approximate energy minimization via graph cuts,” IEEE Trans. Pattern Anal. Machine Intell. 23(11), 1222–1239 (2001).
[Crossref]

J Optim Theory Appl (1)

M. R. Hestenes, “Multiplier and gradient methods,” J Optim Theory Appl 4(5), 303–320 (1969).
[Crossref]

J. Biomed. Opt. (2)

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[Crossref]

S. L. Taylor, S. K. Mason, S. L. Glinton, M. Cobbold, and H. Dehghani, “Accounting for filter bandwidth improves the quantitative accuracy of bioluminescence tomography,” J. Biomed. Opt. 20(9), 096001 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Soc. Ind. Appl. Math. (1)

D. W. Peaceman, J. Rachford, and H. Henry, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955).
[Crossref]

Meas. Sci. Technol. (1)

J. A. Guggenheim, H. R. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24(10), 105405 (2013).
[Crossref]

Med. Phys. (1)

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
[Crossref]

Nat. Photonics (1)

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

Neurosurgery (1)

O. Szentirmai, C. H. Baker, N. Lin, S. Szucs, M. Takahashi, S. Kiryu, A. L. Kung, R. C. Mulligan, and B. S. Carter, “Noninvasive bioluminescence imaging of luciferase expressing intracranial U87 xenografts: correlation with magnetic resonance imaging determined tumor volume and longitudinal use in assessing tumor growth and antiangiogenic treatment effect,” Neurosurgery 58(2), 365–372 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. D (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60(1–4), 259–268 (1992).
[Crossref]

SIAM J. Comput. (1)

M. Cheraghchi, V. Guruswami, and A. Velingker, “Restricted isometry of Fourier matrices and list decodability of random linear codes,” SIAM J. Comput. 42(5), 1888–1914 (2013).
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SIAM Journal on Imaging Sciences (1)

S. Becker, J. Bobin, and E. J. Candès, “NESTA: A fast and accurate first-order method for sparse recovery,” SIAM Journal on Imaging Sciences 4(1), 1–39 (2011).
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SIAM Rev. (1)

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).
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Figures (9)

Fig. 1.
Fig. 1. Examples of the different types of measurements matrices that can be used for image compression. (a) Randomly generated patterns with a Gaussian distribution, (b) Hadamard matrices and (c) a raster scanning method where the scene is scanned pixel by pixel.
Fig. 2.
Fig. 2. (a) Schematic of the developed hyperspectral imaging system, (b) Schematic of the internal components within the DLP used and (c) the random binary patterns that are displayed on the digital micro-mirror device.
Fig. 3.
Fig. 3. Schematic of the phantom setup and the reconstructed surface fluence images for the number of measurements (as a percentage of total pixels) used for reconstruction at 620 nm. Green dashed line represents the outline of the phantom. The ‘ground truth’ image was measured using a raster-scan of 400 measurements.
Fig. 4.
Fig. 4. (a) Maximum reconstructed value for the number of measurements used for reconstruction (solid red) and the maximum value for the ground truth (dashed blue). (b) The percentage error between the reconstructed images and the ground truth for the number of measurements taken.
Fig. 5.
Fig. 5. The surface fluence images reconstructed at a wavelength of 620 nm for different measurement matrix ‘fullness’. Green dashed line represents the outline of the phantom.
Fig. 6.
Fig. 6. (a) Measured maximum reconstructed value for the measurement matrix ‘fullness’ used for reconstruction (solid red) and the maximum value for the ground truth (dashed blue). (b) The percentage error between the reconstructed images and the ground truth for the measurement matrix ‘fullness’ used for reconstruction. (c) The signal-to-noise ratio obtained for each measurement matrix ‘fullness’ used.
Fig. 7.
Fig. 7. 2D cross-sections of the tomographic reconstruction of a 620 nm LED within the block phantom from the (a, d) front view, (b, e) side view and (c, f) top view.
Fig. 8.
Fig. 8. (a) Overlaid image of the recovered surface fluence of the fiber light source inside the mouse shaped phantom. (b) The hyperspectral data collected from the mouse phantom, each colored line represents a measurement using one pattern, the black dashed line represents the emission spectrum of the internal light source. Tomographic reconstruction of the light source from the (c) side, (d) front and (e) top.
Fig. 9.
Fig. 9. (a) Schematic of the phantom setup. (b) RGB color image of the reconstructed surface emission due to the internal LEDs. (c) Emission spectra of the red and green LEDs, the dashed lines represent the wavelengths that measurements were taken for tomographic reconstruction. Each curve represents a measurement taken with an individual random binary pattern. Tomographic reconstructions of the green and red LEDs from the (d) side and (e) top.

Tables (1)

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Table 1. The expected and measured volume of the internal light sources and the localization error of the reconstructed sources.

Equations (5)

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x = i = 1 N s i φ i = φ s
y = ϕ x = ϕ φ s = Θ s
min ( y Θ s 2 2 + λ 2 s 2 2 )
m i n s 1 s u c h t h a t Θ s = y
min i w i , s u c h t h a t ϕ x = y ; D i x = w i