A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[CrossRef]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys. 44, 9 (2011).

[CrossRef]

R. Hofmann, J. Moosmann, and T. Baumbach, “Criticality in single-distance phase retrieval,” Opt. Express 19, 25881–25890 (2011).

[CrossRef]

J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53, 67–92 (2010).

[CrossRef]

X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inv. Probl. and Imaging 2, 455–484 (2008).

[CrossRef]

E. Candes, 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]
[PubMed]

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Proc. 50, 1417–1428 (2003).

[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

G. M. P. van Kemplen and L. J. van Vliet, “The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms,” J. of Microscopy 198, 63–75 (2000).

[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

S.-R. Zhao and H. Halling, “A new Fourier method for fan beam reconstruction,” IEEE Nucl. Sci. Symp. Med. and Imaging Conf. 2, 1287–1291 (1995).

L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).

[CrossRef]

L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).

[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[CrossRef]

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Im. Sci. 2, 183–202 (2009).

[CrossRef]

M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Proc. 50, 1417–1428 (2003).

[CrossRef]

X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inv. Probl. and Imaging 2, 455–484 (2008).

[CrossRef]

E. Candes, 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]

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).

[CrossRef]

X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inv. Probl. and Imaging 2, 455–484 (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]
[PubMed]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys. 44, 9 (2011).

[CrossRef]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “A mixed contrast transfer and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32, 1617–1619 (2007).

[CrossRef]
[PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53, 67–92 (2010).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “A mixed contrast transfer and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32, 1617–1619 (2007).

[CrossRef]
[PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

S.-R. Zhao and H. Halling, “A new Fourier method for fan beam reconstruction,” IEEE Nucl. Sci. Symp. Med. and Imaging Conf. 2, 1287–1291 (1995).

J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53, 67–92 (2010).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53, 67–92 (2010).

[CrossRef]

J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53, 67–92 (2010).

[CrossRef]

A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (IEEE Press, 1988).

A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[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]
[PubMed]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys. 44, 9 (2011).

[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Proc. 50, 1417–1428 (2003).

[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

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]
[PubMed]

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

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys. 44, 9 (2011).

[CrossRef]

E. Candes, 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]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (IEEE Press, 1988).

A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[CrossRef]

E. Candes, 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]

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Im. Sci. 2, 183–202 (2009).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

G. M. P. van Kemplen and L. J. van Vliet, “The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms,” J. of Microscopy 198, 63–75 (2000).

[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

G. M. P. van Kemplen and L. J. van Vliet, “The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms,” J. of Microscopy 198, 63–75 (2000).

[CrossRef]

A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[CrossRef]

M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Proc. 50, 1417–1428 (2003).

[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

S.-R. Zhao and H. Halling, “A new Fourier method for fan beam reconstruction,” IEEE Nucl. Sci. Symp. Med. and Imaging Conf. 2, 1287–1291 (1995).

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).

[CrossRef]

S.-R. Zhao and H. Halling, “A new Fourier method for fan beam reconstruction,” IEEE Nucl. Sci. Symp. Med. and Imaging Conf. 2, 1287–1291 (1995).

E. Candes, 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]

M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Proc. 50, 1417–1428 (2003).

[CrossRef]

X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inv. Probl. and Imaging 2, 455–484 (2008).

[CrossRef]

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).

[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).

[CrossRef]
[PubMed]

G. M. P. van Kemplen and L. J. van Vliet, “The influence of the regularization parameter and the first estimate on the performance of Tikhonov regularized non-linear image restoration algorithms,” J. of Microscopy 198, 63–75 (2000).

[CrossRef]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys. 44, 9 (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]
[PubMed]

J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg. 53, 67–92 (2010).

[CrossRef]

A. Kostenko, K.J. Batenburg, H. Suhonen, S.E. Offerman, and L.J. van Vliet, “Phase retrieval in in-line x-ray phase-contrast imaging based on total variation minimization,” Opt. Expr. 21, 710–723 (2013).

[CrossRef]

X. Wu and A. Yan, “Phase retrieval from one single phase-contrast x-ray image,” Opt. Express 17, 11187 (2009).

[CrossRef]
[PubMed]

R. Hofmann, J. Moosmann, and T. Baumbach, “Criticality in single-distance phase retrieval,” Opt. Express 19, 25881–25890 (2011).

[CrossRef]

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express 12, 2960–2965 (2004).

[CrossRef]
[PubMed]

L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).

[CrossRef]

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Im. Sci. 2, 183–202 (2009).

[CrossRef]

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

A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (IEEE Press, 1988).