P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2D tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).

[CrossRef]

S. H. Izen, “Sampling in flat detector fan beam tomography,” SIAM J. Appl. Math. 72, 61–84 (2012).

[CrossRef]

D. Brady and D. Marks, “Coding for compressive focal tomography,” Appl. Opt. 50, 4436–4449 (2011).

[CrossRef]

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19, 7289–7298 (2011).

[CrossRef]

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Video rate spectral imaging using a coded aperture snapshot spectral imager,” Opt. Express 17, 6368–6388 (2009).

[CrossRef]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).

[CrossRef]

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).

[CrossRef]

E. Y. Sidky and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).

[CrossRef]

G. H. Chen, J. Tang, and S. H. Leng, “Prior image constrained compressed sensing: a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35, 660–663 (2008).

[CrossRef]

E. Hansis, D. Schafer, O. Dossel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27, 1548–1555 (2008).

[CrossRef]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).

[CrossRef]

J. A. O’Sullivan and J. Benac, “Alternating minimization algorithms for transmission tomography,” IEEE Trans. Med. Imaging 26, 283–297 (2007).

[CrossRef]

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy k-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).

[CrossRef]

J. Song, Q. H. Liu, G. A. Johnson, and C. T. Badea, “Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT,” Med. Phys. 34, 4476–4483 (2007).

[CrossRef]

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).

[CrossRef]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).

[CrossRef]

J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 52, 1030–1051 (2006).

[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).

[CrossRef]

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).

[CrossRef]

G.-H. Chen, S. Leng, and C. A. Mistretta, “A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections,” Med. Phys. 32, 654–665 (2005).

[CrossRef]

D. J. Brady, N. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21, 1140–1147 (2004).

[CrossRef]

R. Ning, X. Tang, and D. Conover, “X-ray scatter correction algorithm for cone beam CT imaging,” Med. Phys. 31, 1195–1202 (2004).

[CrossRef]

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization,” Proc. Natl. Acad. Sci. USA 100, 2197–2202 (2003).

[CrossRef]

R. Ning, X. Tang, and D. L. Conover, “X-ray scatter suppression algorithm for cone-beam volume CT,” Proc. SPIE 4685, 774–781 (2002).

[CrossRef]

M. H. Li, H. Q. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).

[CrossRef]

M. E. Tipping, “Sparse Bayesian learning and the relevance vector machine,” J. Mach. Learn. Res. 1, 211–244 (2001).

H. Strecker, “Automatic detection of explosives in airline baggage using elastic x-ray scatter,” Medicamundi 42, 30–33 (1998).

F. Natterer, “Sampling in fan beam tomography,” SIAM J. Appl. Math. 53, 358–380 (1993).

[CrossRef]

H. Peng and H. Stark, “Direct fourier reconstruction in fan-beam tomography,” IEEE Trans. Med. Imaging 6, 209–219 (1987).

[CrossRef]

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).

[CrossRef]

A. K. Louis, “Incomplete data problems in x-ray computerized tomography,” Numer. Math. 48, 251–262 (1986).

[CrossRef]

M. E. Davison, “The ill-conditioned nature of the limited angle tomography problem,” SIAM J. Appl. Math. 43, 428–448 (1983).

[CrossRef]

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: part 1 theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).

[CrossRef]

M. I. Sezan and H. Stark, “Image restoration by the method of convex projections: part 2 applications and numerical results,” IEEE Trans. Med. Imaging 1, 95–101 (1982).

[CrossRef]

A. G. Lindgren and P. A. Rattey, “The inverse discrete Radon transform with applications to tomographic imaging using projection data,” Adv. Electron. Electron Phys. 56, 359–410 (1981).

[CrossRef]

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces,” Inf. Control 5, 279–323 (1962).

[CrossRef]

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

J. Song, Q. H. Liu, G. A. Johnson, and C. T. Badea, “Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT,” Med. Phys. 34, 4476–4483 (2007).

[CrossRef]

J. A. O’Sullivan and J. Benac, “Alternating minimization algorithms for transmission tomography,” IEEE Trans. Med. Imaging 26, 283–297 (2007).

[CrossRef]

J. M. Bernardo and A. F. Smith, Bayesian Theory, Vol. 405 of Wiley Series in Probability and Statistics (Wiley, 2009).

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2D tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).

[CrossRef]

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19, 7289–7298 (2011).

[CrossRef]

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Video rate spectral imaging using a coded aperture snapshot spectral imager,” Opt. Express 17, 6368–6388 (2009).

[CrossRef]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).

[CrossRef]

D. J. Brady, N. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21, 1140–1147 (2004).

[CrossRef]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).

[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).

[CrossRef]

G. H. Chen, J. Tang, and S. H. Leng, “Prior image constrained compressed sensing: a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35, 660–663 (2008).

[CrossRef]

G.-H. Chen, S. Leng, and C. A. Mistretta, “A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections,” Med. Phys. 32, 654–665 (2005).

[CrossRef]

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19, 7289–7298 (2011).

[CrossRef]

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).

[CrossRef]

R. Ning, X. Tang, and D. Conover, “X-ray scatter correction algorithm for cone beam CT imaging,” Med. Phys. 31, 1195–1202 (2004).

[CrossRef]

R. Ning, X. Tang, and D. L. Conover, “X-ray scatter suppression algorithm for cone-beam volume CT,” Proc. SPIE 4685, 774–781 (2002).

[CrossRef]

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

C. Cozzini, S. Olesinski, and G. Harding, “Modeling scattering for security applications: a multiple beam x-ray diffraction imaging system,” in IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (IEEE, 2012), pp. 74–77.

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy k-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).

[CrossRef]

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012), Chap. 1.

M. E. Davison, “The ill-conditioned nature of the limited angle tomography problem,” SIAM J. Appl. Math. 43, 428–448 (1983).

[CrossRef]

C. W. Dodge, A Rapid Method for the Simulation of Filtered X-Ray Spectra in Diagnostic Imaging Systems (ProQuest, 2008).

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).

[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).

[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).

[CrossRef]

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization,” Proc. Natl. Acad. Sci. USA 100, 2197–2202 (2003).

[CrossRef]

E. Hansis, D. Schafer, O. Dossel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27, 1548–1555 (2008).

[CrossRef]

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012), Chap. 1.

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization,” Proc. Natl. Acad. Sci. USA 100, 2197–2202 (2003).

[CrossRef]

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012), Chap. 1.

M. Sonka and J. M. Fitzpatrick, Handbook of Medical Imaging, Vol. 2 of Medical Image Processing and Analysis (SPIE, 2000).

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

E. Hansis, D. Schafer, O. Dossel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27, 1548–1555 (2008).

[CrossRef]

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

E. Hansis, D. Schafer, O. Dossel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27, 1548–1555 (2008).

[CrossRef]

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).

[CrossRef]

C. Cozzini, S. Olesinski, and G. Harding, “Modeling scattering for security applications: a multiple beam x-ray diffraction imaging system,” in IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (IEEE, 2012), pp. 74–77.

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

G. T. Herman, Image Reconstruction from Projections (Academic, 1980).

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE, 2009).

S. H. Izen, “Sampling in flat detector fan beam tomography,” SIAM J. Appl. Math. 72, 61–84 (2012).

[CrossRef]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).

[CrossRef]

J. Song, Q. H. Liu, G. A. Johnson, and C. T. Badea, “Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT,” Med. Phys. 34, 4476–4483 (2007).

[CrossRef]

M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (SIAM, 1988).

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).

[CrossRef]

F. Krahmer and R. Ward, “Beyond incoherence: stable and robust sampling strategies for compressive imaging,” arXiv:1210.2380 (2012).

M. H. Li, H. Q. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).

[CrossRef]

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012), Chap. 1.

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

G.-H. Chen, S. Leng, and C. A. Mistretta, “A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections,” Med. Phys. 32, 654–665 (2005).

[CrossRef]

G. H. Chen, J. Tang, and S. H. Leng, “Prior image constrained compressed sensing: a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35, 660–663 (2008).

[CrossRef]

M. H. Li, H. Q. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

A. G. Lindgren and P. A. Rattey, “The inverse discrete Radon transform with applications to tomographic imaging using projection data,” Adv. Electron. Electron Phys. 56, 359–410 (1981).

[CrossRef]

J. Song, Q. H. Liu, G. A. Johnson, and C. T. Badea, “Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT,” Med. Phys. 34, 4476–4483 (2007).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

A. K. Louis, “Incomplete data problems in x-ray computerized tomography,” Numer. Math. 48, 251–262 (1986).

[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).

[CrossRef]

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).

[CrossRef]

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy k-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).

[CrossRef]

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces,” Inf. Control 5, 279–323 (1962).

[CrossRef]

G.-H. Chen, S. Leng, and C. A. Mistretta, “A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections,” Med. Phys. 32, 654–665 (2005).

[CrossRef]

F. Natterer, “Sampling in fan beam tomography,” SIAM J. Appl. Math. 53, 358–380 (1993).

[CrossRef]

F. Natterer, The Mathematics of Computerized Tomography (Wiley, 1986).

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).

[CrossRef]

R. Ning, X. Tang, and D. Conover, “X-ray scatter correction algorithm for cone beam CT imaging,” Med. Phys. 31, 1195–1202 (2004).

[CrossRef]

R. Ning, X. Tang, and D. L. Conover, “X-ray scatter suppression algorithm for cone-beam volume CT,” Proc. SPIE 4685, 774–781 (2002).

[CrossRef]

J. A. O’Sullivan and J. Benac, “Alternating minimization algorithms for transmission tomography,” IEEE Trans. Med. Imaging 26, 283–297 (2007).

[CrossRef]

C. Cozzini, S. Olesinski, and G. Harding, “Modeling scattering for security applications: a multiple beam x-ray diffraction imaging system,” in IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (IEEE, 2012), pp. 74–77.

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

E. Y. Sidky and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).

[CrossRef]

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).

[CrossRef]

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).

[CrossRef]

H. Peng and H. Stark, “Direct fourier reconstruction in fan-beam tomography,” IEEE Trans. Med. Imaging 6, 209–219 (1987).

[CrossRef]

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces,” Inf. Control 5, 279–323 (1962).

[CrossRef]

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

A. G. Lindgren and P. A. Rattey, “The inverse discrete Radon transform with applications to tomographic imaging using projection data,” Adv. Electron. Electron Phys. 56, 359–410 (1981).

[CrossRef]

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).

[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

E. Hansis, D. Schafer, O. Dossel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27, 1548–1555 (2008).

[CrossRef]

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

M. I. Sezan and H. Stark, “Image restoration by the method of convex projections: part 2 applications and numerical results,” IEEE Trans. Med. Imaging 1, 95–101 (1982).

[CrossRef]

E. Y. Sidky and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).

[CrossRef]

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (SIAM, 1988).

J. M. Bernardo and A. F. Smith, Bayesian Theory, Vol. 405 of Wiley Series in Probability and Statistics (Wiley, 2009).

F. Smith, Industrial Applications of X-Ray Diffraction (CRC Press, 1999).

J. Song, Q. H. Liu, G. A. Johnson, and C. T. Badea, “Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT,” Med. Phys. 34, 4476–4483 (2007).

[CrossRef]

M. Sonka and J. M. Fitzpatrick, Handbook of Medical Imaging, Vol. 2 of Medical Image Processing and Analysis (SPIE, 2000).

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

H. Peng and H. Stark, “Direct fourier reconstruction in fan-beam tomography,” IEEE Trans. Med. Imaging 6, 209–219 (1987).

[CrossRef]

M. I. Sezan and H. Stark, “Image restoration by the method of convex projections: part 2 applications and numerical results,” IEEE Trans. Med. Imaging 1, 95–101 (1982).

[CrossRef]

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

H. Strecker, “Automatic detection of explosives in airline baggage using elastic x-ray scatter,” Medicamundi 42, 30–33 (1998).

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Video rate spectral imaging using a coded aperture snapshot spectral imager,” Opt. Express 17, 6368–6388 (2009).

[CrossRef]

D. J. Brady, N. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21, 1140–1147 (2004).

[CrossRef]

G. H. Chen, J. Tang, and S. H. Leng, “Prior image constrained compressed sensing: a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35, 660–663 (2008).

[CrossRef]

R. Ning, X. Tang, and D. Conover, “X-ray scatter correction algorithm for cone beam CT imaging,” Med. Phys. 31, 1195–1202 (2004).

[CrossRef]

R. Ning, X. Tang, and D. L. Conover, “X-ray scatter suppression algorithm for cone-beam volume CT,” Proc. SPIE 4685, 774–781 (2002).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).

[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

M. E. Tipping, “Sparse Bayesian learning and the relevance vector machine,” J. Mach. Learn. Res. 1, 211–244 (2001).

K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2D tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).

[CrossRef]

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy k-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).

[CrossRef]

J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 52, 1030–1051 (2006).

[CrossRef]

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

F. Krahmer and R. Ward, “Beyond incoherence: stable and robust sampling strategies for compressive imaging,” arXiv:1210.2380 (2012).

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: part 1 theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).

[CrossRef]

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).

[CrossRef]

M. H. Li, H. Q. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: part 1 theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

A. G. Lindgren and P. A. Rattey, “The inverse discrete Radon transform with applications to tomographic imaging using projection data,” Adv. Electron. Electron Phys. 56, 359–410 (1981).

[CrossRef]

R. Rangayyan, A. P. Dhawan, and R. Gordon, “Algorithms for limited-view computed-tomography—an annotated bibliography and a challenge,” Appl. Opt. 24, 4000–4012 (1985).

[CrossRef]

K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2D tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).

[CrossRef]

D. Brady and D. Marks, “Coding for compressive focal tomography,” Appl. Opt. 50, 4436–4449 (2011).

[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).

[CrossRef]

M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI,” IEEE Signal Process. Mag. 25(2), 72–82 (2008).

[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).

[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).

[CrossRef]

J. A. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 52, 1030–1051 (2006).

[CrossRef]

M. I. Sezan and H. Stark, “Image restoration by the method of convex projections: part 2 applications and numerical results,” IEEE Trans. Med. Imaging 1, 95–101 (1982).

[CrossRef]

D. C. Youla and H. Webb, “Image restoration by the method of convex projections: part 1 theory,” IEEE Trans. Med. Imaging 1, 81–94 (1982).

[CrossRef]

E. Hansis, D. Schafer, O. Dossel, and M. Grass, “Evaluation of iterative sparse object reconstruction from few projections for 3-D rotational coronary angiography,” IEEE Trans. Med. Imaging 27, 1548–1555 (2008).

[CrossRef]

J. A. O’Sullivan and J. Benac, “Alternating minimization algorithms for transmission tomography,” IEEE Trans. Med. Imaging 26, 283–297 (2007).

[CrossRef]

H. Peng and H. Stark, “Direct fourier reconstruction in fan-beam tomography,” IEEE Trans. Med. Imaging 6, 209–219 (1987).

[CrossRef]

S. Pani, E. Cook, J. Horrocks, L. George, S. Hardwick, and R. Speller, “Modelling an energy-dispersive x-ray diffraction system for drug detection,” IEEE Trans. Nucl. Sci. 56, 1238–1241 (2009).

[CrossRef]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).

[CrossRef]

D. P. Petersen and D. Middleton, “Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces,” Inf. Control 5, 279–323 (1962).

[CrossRef]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).

[CrossRef]

M. E. Tipping, “Sparse Bayesian learning and the relevance vector machine,” J. Mach. Learn. Res. 1, 211–244 (2001).

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 119–139 (2006).

M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson. Med. 58, 1182–1195 (2007).

[CrossRef]

J. Song, Q. H. Liu, G. A. Johnson, and C. T. Badea, “Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT,” Med. Phys. 34, 4476–4483 (2007).

[CrossRef]

G.-H. Chen, S. Leng, and C. A. Mistretta, “A novel extension of the parallel-beam projection-slice theorem to divergent fan-beam and cone-beam projections,” Med. Phys. 32, 654–665 (2005).

[CrossRef]

G. H. Chen, J. Tang, and S. H. Leng, “Prior image constrained compressed sensing: a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35, 660–663 (2008).

[CrossRef]

K. Choi, J. Wang, L. Zhu, T. S. Suh, S. Boyd, and L. Xing, “Compressed sensing based cone-beam computed tomography reconstruction with a first-order method,” Med. Phys. 37, 5113–5125 (2010).

[CrossRef]

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).

[CrossRef]

R. Ning, X. Tang, and D. Conover, “X-ray scatter correction algorithm for cone beam CT imaging,” Med. Phys. 31, 1195–1202 (2004).

[CrossRef]

H. Strecker, “Automatic detection of explosives in airline baggage using elastic x-ray scatter,” Medicamundi 42, 30–33 (1998).

A. K. Louis, “Incomplete data problems in x-ray computerized tomography,” Numer. Math. 48, 251–262 (1986).

[CrossRef]

A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, “Video rate spectral imaging using a coded aperture snapshot spectral imager,” Opt. Express 17, 6368–6388 (2009).

[CrossRef]

P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, “Coded aperture compressive temporal imaging,” Opt. Express 21, 10526–10545 (2013).

[CrossRef]

J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19, 7289–7298 (2011).

[CrossRef]

E. Y. Sidky and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).

[CrossRef]

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy k-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).

[CrossRef]

M. H. Li, H. Q. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).

[CrossRef]

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization,” Proc. Natl. Acad. Sci. USA 100, 2197–2202 (2003).

[CrossRef]

R. Ning, X. Tang, and D. L. Conover, “X-ray scatter suppression algorithm for cone-beam volume CT,” Proc. SPIE 4685, 774–781 (2002).

[CrossRef]

J. W. Stayman, W. Zbijewski, Y. Otake, A. Uneri, S. Schafer, J. Lee, J. L. Prince, and J. H. Siewerdsen, “Penalized-likelihood reconstruction for sparse data acquisitions with unregistered prior images and compressed sensing penalties,” Proc. SPIE 7961, 79611L (2011).

[CrossRef]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).

[CrossRef]

F. Natterer, “Sampling in fan beam tomography,” SIAM J. Appl. Math. 53, 358–380 (1993).

[CrossRef]

M. E. Davison, “The ill-conditioned nature of the limited angle tomography problem,” SIAM J. Appl. Math. 43, 428–448 (1983).

[CrossRef]

S. H. Izen, “Sampling in flat detector fan beam tomography,” SIAM J. Appl. Math. 72, 61–84 (2012).

[CrossRef]

F. Natterer, The Mathematics of Computerized Tomography (Wiley, 1986).

M. Slaney and A. Kak, Principles of Computerized Tomographic Imaging (SIAM, 1988).

http://www.mathworks.com/matlabcentral/fileexchange/27375-plot-wavelet-image-2d-decomposition/content/plotwavelet2.m .

M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Introduction to compressed sensing,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012), Chap. 1.

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE, 2009).

F. Krahmer and R. Ward, “Beyond incoherence: stable and robust sampling strategies for compressive imaging,” arXiv:1210.2380 (2012).

J. M. Bernardo and A. F. Smith, Bayesian Theory, Vol. 405 of Wiley Series in Probability and Statistics (Wiley, 2009).

C. W. Dodge, A Rapid Method for the Simulation of Filtered X-Ray Spectra in Diagnostic Imaging Systems (ProQuest, 2008).

C. Cozzini, S. Olesinski, and G. Harding, “Modeling scattering for security applications: a multiple beam x-ray diffraction imaging system,” in IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (IEEE, 2012), pp. 74–77.

B. Adcock, A. C. Hansen, C. Poon, and B. Roman, “Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing,” arXiv:1302.0561 (2013).

G. T. Herman, Image Reconstruction from Projections (Academic, 1980).

F. Smith, Industrial Applications of X-Ray Diffraction (CRC Press, 1999).

M. Sonka and J. M. Fitzpatrick, Handbook of Medical Imaging, Vol. 2 of Medical Image Processing and Analysis (SPIE, 2000).