T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking
morphological dynamics,” Proc. Natl. Acad. Sci.
USA 111, 3921–3926 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[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.
Express 21, 710–723 (2013).

[Crossref]
[PubMed]

L. Reichel and G. Rodriguez, “Old and new parameter choice rules for discrete
ill-posed problems,” Numer. Algorithms 63, 65–87 (2013).

[Crossref]

P. T. Lauzier, J. Tang, and G. Chen, “Prior image constrained compressed sensing:
Implementation and performance evaluation,” Med.
Phys. 39, 66–80 (2012).

[Crossref]
[PubMed]

Y. Hu and M. Jacob, “Higher degree total variation (HDTV)
regularization for image recovery,” IEEE Trans.
Image Process. 21, 2559–2571 (2012).

[Crossref]
[PubMed]

T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method
for strongly convex total variation regularization,” BIT 52, 329–356 (2012).

[Crossref]

T. van de Kamp, P. Vagovič, T. Baumbach, and A. Riedel, “A biological screw in a beetle’s
leg,” Science 333, 52 (2011).

[Crossref]

J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase
shifts,” Opt. Express 19, 12066–12073 (2011).

[Crossref]
[PubMed]

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

[Crossref]

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

[Crossref]

J. Yang, Y. Zhang, and W. Yin, “A fast alternating direction method for TVL1-L2
signal reconstruction from partial Fourier data,” IEEE J. Sel. Top. Signa. 4, 288–297 (2010).

[Crossref]

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

[Crossref]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized
problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

[Crossref]

E. Esser, “Applications of Lagrangian-based alternating
direction methods and connections to split Bregman,” CAM Report 9, 31 (2009).

Z. Wang and A. C. Bovik, “Mean squared error: love it or leave it? A new
look at signal fidelity measures,” IEEE Signal Proc.
Mag. 26, 98–117 (2009).

[Crossref]

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for
total variation image reconstruction,” SIAM J.
Imaging Sci. 1, 248–272 (2008).

[Crossref]

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

[Crossref]
[PubMed]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage /
thresholding algorithms for image restoration,” IEEE
Trans. Image Process. 16, 2992–3004 (2007).

[Crossref]
[PubMed]

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]
[PubMed]

J. Song, Q. 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]
[PubMed]

W. W. Hager and H. Zhang, “A survey of nonlinear conjugate gradient
methods,” Pac. J. Optim. 2, 35–58 (2006).

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

[Crossref]

T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent developments in total variation image
restoration,” Mathematical Models of Computer
Vision 2005,17 (2005).

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility
to structural similarity,” IEEE Trans. Image
Process. 13, 600–612 (2004).

[Crossref]
[PubMed]

D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari, “Tikhonov regularization and the L-curve for
large discrete ill-posed problems,” J. Comput. Appl.
Math. 123, 423–446 (2000).

[Crossref]

Y. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a
strong global convergence property,” SIAM J.
Optimiz. 10, 177–182 (1999).

[Crossref]

C. R. Vogel, “Non-convergence of the L-curve regularization
parameter selection method,” Inverse Probl. 12, 535 (1996).

[Crossref]

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of
discrete ill-posed problems,” SIAM J. Sci.
Comput. 14, 1487–1503 (1993).

[Crossref]

M. Fukushima, “Application of the alternating direction method
of multipliers to separable convex programming problems,” Comput. Optim. Appl. 1, 93–111 (1992).

[Crossref]

R. L. Siddon, “Fast calculation of the exact radiological path
for a three-dimensional CT array,” Med.
Phys. 12, 252–255 (1985).

[Crossref]
[PubMed]

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for
choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).

[Crossref]

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for
three-dimensional electron microscopy and X-ray
photography,” J. Theor. Biol. 29, 471–481 (1970).

[Crossref]
[PubMed]

V. A. Morozov, “On the solution of functional equations by the
method of regularization,” “Soviet Math.
Dokl,”, 7, pp. 414–417 (1966.

S. Kaczmarz, “Angenäherte Auflösung von Systemen Linearer
Gleichungen,” Bulletin International de l’Academie
Polonaise des Sciences et des Lettres 35, 355–357 (1937).

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

J. Song, Q. 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]
[PubMed]

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking
morphological dynamics,” Proc. Natl. Acad. Sci.
USA 111, 3921–3926 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

T. van de Kamp, P. Vagovič, T. Baumbach, and A. Riedel, “A biological screw in a beetle’s
leg,” Science 333, 52 (2011).

[Crossref]

J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase
shifts,” Opt. Express 19, 12066–12073 (2011).

[Crossref]
[PubMed]

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

[Crossref]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

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

[Crossref]

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

[Crossref]

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for
three-dimensional electron microscopy and X-ray
photography,” J. Theor. Biol. 29, 471–481 (1970).

[Crossref]
[PubMed]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage /
thresholding algorithms for image restoration,” IEEE
Trans. Image Process. 16, 2992–3004 (2007).

[Crossref]
[PubMed]

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

[Crossref]

Z. Wang and A. C. Bovik, “Mean squared error: love it or leave it? A new
look at signal fidelity measures,” IEEE Signal Proc.
Mag. 26, 98–117 (2009).

[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility
to structural similarity,” IEEE Trans. Image
Process. 13, 600–612 (2004).

[Crossref]
[PubMed]

D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari, “Tikhonov regularization and the L-curve for
large discrete ill-posed problems,” J. Comput. Appl.
Math. 123, 423–446 (2000).

[Crossref]

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

[Crossref]

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

[Crossref]

T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent developments in total variation image
restoration,” Mathematical Models of Computer
Vision 2005,17 (2005).

P. T. Lauzier, J. Tang, and G. Chen, “Prior image constrained compressed sensing:
Implementation and performance evaluation,” Med.
Phys. 39, 66–80 (2012).

[Crossref]
[PubMed]

Y. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a
strong global convergence property,” SIAM J.
Optimiz. 10, 177–182 (1999).

[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]
[PubMed]

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking
morphological dynamics,” Proc. Natl. Acad. Sci.
USA 111, 3921–3926 (2014).

[Crossref]
[PubMed]

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking
morphological dynamics,” Proc. Natl. Acad. Sci.
USA 111, 3921–3926 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent developments in total variation image
restoration,” Mathematical Models of Computer
Vision 2005,17 (2005).

E. Esser, “Applications of Lagrangian-based alternating
direction methods and connections to split Bregman,” CAM Report 9, 31 (2009).

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage /
thresholding algorithms for image restoration,” IEEE
Trans. Image Process. 16, 2992–3004 (2007).

[Crossref]
[PubMed]

M. Fukushima, “Application of the alternating direction method
of multipliers to separable convex programming problems,” Comput. Optim. Appl. 1, 93–111 (1992).

[Crossref]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized
problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

[Crossref]

T. Goldstein, B. O’Donoghue, and S. Setzer, “Fast alternating direction optimization
methods,” CAM report pp. 12–35 (2012).

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for
choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).

[Crossref]

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for
three-dimensional electron microscopy and X-ray
photography,” J. Theor. Biol. 29, 471–481 (1970).

[Crossref]
[PubMed]

W. W. Hager and H. Zhang, “A survey of nonlinear conjugate gradient
methods,” Pac. J. Optim. 2, 35–58 (2006).

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method
for strongly convex total variation regularization,” BIT 52, 329–356 (2012).

[Crossref]

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of
discrete ill-posed problems,” SIAM J. Sci.
Comput. 14, 1487–1503 (1993).

[Crossref]

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for
choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).

[Crossref]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for
three-dimensional electron microscopy and X-ray
photography,” J. Theor. Biol. 29, 471–481 (1970).

[Crossref]
[PubMed]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase
shifts,” Opt. Express 19, 12066–12073 (2011).

[Crossref]
[PubMed]

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

[Crossref]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

G. N. Hounsfield, “A method and apparatus for examination of a body by
radiation such as X-ray or gamma radiation,” (1972). Patent Specification 1283915.

Y. Hu and M. Jacob, “Higher degree total variation (HDTV)
regularization for image recovery,” IEEE Trans.
Image Process. 21, 2559–2571 (2012).

[Crossref]
[PubMed]

Y. Hu and M. Jacob, “Higher degree total variation (HDTV)
regularization for image recovery,” IEEE Trans.
Image Process. 21, 2559–2571 (2012).

[Crossref]
[PubMed]

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method
for strongly convex total variation regularization,” BIT 52, 329–356 (2012).

[Crossref]

T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method
for strongly convex total variation regularization,” BIT 52, 329–356 (2012).

[Crossref]

J. Song, Q. 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]
[PubMed]

T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method
for strongly convex total variation regularization,” BIT 52, 329–356 (2012).

[Crossref]

S. Kaczmarz, “Angenäherte Auflösung von Systemen Linearer
Gleichungen,” Bulletin International de l’Academie
Polonaise des Sciences et des Lettres 35, 355–357 (1937).

A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (Society for Industrial and Applied Mathematics, 2001).

[Crossref]

E. Y. Sidky, C. Kao, and X. 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. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

P. T. Lauzier, J. Tang, and G. Chen, “Prior image constrained compressed sensing:
Implementation and performance evaluation,” Med.
Phys. 39, 66–80 (2012).

[Crossref]
[PubMed]

C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented
lagrangian and alternating direction algorithms,” CAAM Report (2009).

C. Li, Compressive Sensing for 3D Data Processing
Tasks: Applications, Models and Algorithms, (PhD
Thesis in Rice University, 2011).

J. Song, Q. 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]
[PubMed]

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]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

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

[Crossref]

J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase
shifts,” Opt. Express 19, 12066–12073 (2011).

[Crossref]
[PubMed]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari, “Tikhonov regularization and the L-curve for
large discrete ill-posed problems,” J. Comput. Appl.
Math. 123, 423–446 (2000).

[Crossref]

V. A. Morozov, “On the solution of functional equations by the
method of regularization,” “Soviet Math.
Dokl,”, 7, pp. 414–417 (1966.

T. Goldstein, B. O’Donoghue, and S. Setzer, “Fast alternating direction optimization
methods,” CAM report pp. 12–35 (2012).

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of
discrete ill-posed problems,” SIAM J. Sci.
Comput. 14, 1487–1503 (1993).

[Crossref]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized
problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

[Crossref]

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

[Crossref]
[PubMed]

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

T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent developments in total variation image
restoration,” Mathematical Models of Computer
Vision 2005,17 (2005).

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

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]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

L. Reichel and G. Rodriguez, “Old and new parameter choice rules for discrete
ill-posed problems,” Numer. Algorithms 63, 65–87 (2013).

[Crossref]

D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari, “Tikhonov regularization and the L-curve for
large discrete ill-posed problems,” J. Comput. Appl.
Math. 123, 423–446 (2000).

[Crossref]

T. van de Kamp, P. Vagovič, T. Baumbach, and A. Riedel, “A biological screw in a beetle’s
leg,” Science 333, 52 (2011).

[Crossref]

L. Reichel and G. Rodriguez, “Old and new parameter choice rules for discrete
ill-posed problems,” Numer. Algorithms 63, 65–87 (2013).

[Crossref]

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

[Crossref]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

T. Goldstein, B. O’Donoghue, and S. Setzer, “Fast alternating direction optimization
methods,” CAM report pp. 12–35 (2012).

D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari, “Tikhonov regularization and the L-curve for
large discrete ill-posed problems,” J. Comput. Appl.
Math. 123, 423–446 (2000).

[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility
to structural similarity,” IEEE Trans. Image
Process. 13, 600–612 (2004).

[Crossref]
[PubMed]

R. L. Siddon, “Fast calculation of the exact radiological path
for a three-dimensional CT array,” Med.
Phys. 12, 252–255 (1985).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

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

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility
to structural similarity,” IEEE Trans. Image
Process. 13, 600–612 (2004).

[Crossref]
[PubMed]

A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (Society for Industrial and Applied Mathematics, 2001).

[Crossref]

J. Song, Q. 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]
[PubMed]

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

X. Tai and C. Wu, “Augmented Lagrangian method, dual methods and
split Bregman iteration for ROF model,” in “Scale
Space and Variational Methods in Computer Vision,” (Springer, 2009), pp. 502–513.

[Crossref]

P. T. Lauzier, J. Tang, and G. Chen, “Prior image constrained compressed sensing:
Implementation and performance evaluation,” Med.
Phys. 39, 66–80 (2012).

[Crossref]
[PubMed]

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

[Crossref]

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

[Crossref]

T. van de Kamp, P. Vagovič, T. Baumbach, and A. Riedel, “A biological screw in a beetle’s
leg,” Science 333, 52 (2011).

[Crossref]

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking
morphological dynamics,” Proc. Natl. Acad. Sci.
USA 111, 3921–3926 (2014).

[Crossref]
[PubMed]

T. van de Kamp, P. Vagovič, T. Baumbach, and A. Riedel, “A biological screw in a beetle’s
leg,” Science 333, 52 (2011).

[Crossref]

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

C. R. Vogel, “Non-convergence of the L-curve regularization
parameter selection method,” Inverse Probl. 12, 535 (1996).

[Crossref]

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for
choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).

[Crossref]

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for
total variation image reconstruction,” SIAM J.
Imaging Sci. 1, 248–272 (2008).

[Crossref]

Z. Wang and A. C. Bovik, “Mean squared error: love it or leave it? A new
look at signal fidelity measures,” IEEE Signal Proc.
Mag. 26, 98–117 (2009).

[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility
to structural similarity,” IEEE Trans. Image
Process. 13, 600–612 (2004).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

X. Tai and C. Wu, “Augmented Lagrangian method, dual methods and
split Bregman iteration for ROF model,” in “Scale
Space and Variational Methods in Computer Vision,” (Springer, 2009), pp. 502–513.

[Crossref]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

J. Yang, Y. Zhang, and W. Yin, “A fast alternating direction method for TVL1-L2
signal reconstruction from partial Fourier data,” IEEE J. Sel. Top. Signa. 4, 288–297 (2010).

[Crossref]

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for
total variation image reconstruction,” SIAM J.
Imaging Sci. 1, 248–272 (2008).

[Crossref]

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

J. Yang, Y. Zhang, and W. Yin, “A fast alternating direction method for TVL1-L2
signal reconstruction from partial Fourier data,” IEEE J. Sel. Top. Signa. 4, 288–297 (2010).

[Crossref]

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for
total variation image reconstruction,” SIAM J.
Imaging Sci. 1, 248–272 (2008).

[Crossref]

C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented
lagrangian and alternating direction algorithms,” CAAM Report (2009).

T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent developments in total variation image
restoration,” Mathematical Models of Computer
Vision 2005,17 (2005).

Y. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a
strong global convergence property,” SIAM J.
Optimiz. 10, 177–182 (1999).

[Crossref]

W. W. Hager and H. Zhang, “A survey of nonlinear conjugate gradient
methods,” Pac. J. Optim. 2, 35–58 (2006).

J. Yang, Y. Zhang, and W. Yin, “A fast alternating direction method for TVL1-L2
signal reconstruction from partial Fourier data,” IEEE J. Sel. Top. Signa. 4, 288–297 (2010).

[Crossref]

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for
total variation image reconstruction,” SIAM J.
Imaging Sci. 1, 248–272 (2008).

[Crossref]

C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented
lagrangian and alternating direction algorithms,” CAAM Report (2009).

T. L. Jensen, J. H. Jørgensen, P. C. Hansen, and S. H. Jensen, “Implementation of an optimal first-order method
for strongly convex total variation regularization,” BIT 52, 329–356 (2012).

[Crossref]

S. Kaczmarz, “Angenäherte Auflösung von Systemen Linearer
Gleichungen,” Bulletin International de l’Academie
Polonaise des Sciences et des Lettres 35, 355–357 (1937).

E. Esser, “Applications of Lagrangian-based alternating
direction methods and connections to split Bregman,” CAM Report 9, 31 (2009).

M. Fukushima, “Application of the alternating direction method
of multipliers to separable convex programming problems,” Comput. Optim. Appl. 1, 93–111 (1992).

[Crossref]

J. Yang, Y. Zhang, and W. Yin, “A fast alternating direction method for TVL1-L2
signal reconstruction from partial Fourier data,” IEEE J. Sel. Top. Signa. 4, 288–297 (2010).

[Crossref]

Z. Wang and A. C. Bovik, “Mean squared error: love it or leave it? A new
look at signal fidelity measures,” IEEE Signal Proc.
Mag. 26, 98–117 (2009).

[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility
to structural similarity,” IEEE Trans. Image
Process. 13, 600–612 (2004).

[Crossref]
[PubMed]

Y. Hu and M. Jacob, “Higher degree total variation (HDTV)
regularization for image recovery,” IEEE Trans.
Image Process. 21, 2559–2571 (2012).

[Crossref]
[PubMed]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage /
thresholding algorithms for image restoration,” IEEE
Trans. Image Process. 16, 2992–3004 (2007).

[Crossref]
[PubMed]

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

[Crossref]

C. R. Vogel, “Non-convergence of the L-curve regularization
parameter selection method,” Inverse Probl. 12, 535 (1996).

[Crossref]

D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari, “Tikhonov regularization and the L-curve for
large discrete ill-posed problems,” J. Comput. Appl.
Math. 123, 423–446 (2000).

[Crossref]

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for
three-dimensional electron microscopy and X-ray
photography,” J. Theor. Biol. 29, 471–481 (1970).

[Crossref]
[PubMed]

E. Y. Sidky, C. Kao, and X. 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]
[PubMed]

T. Chan, S. Esedoglu, F. Park, and A. Yip, “Recent developments in total variation image
restoration,” Mathematical Models of Computer
Vision 2005,17 (2005).

J. Song, Q. 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]
[PubMed]

P. T. Lauzier, J. Tang, and G. Chen, “Prior image constrained compressed sensing:
Implementation and performance evaluation,” Med.
Phys. 39, 66–80 (2012).

[Crossref]
[PubMed]

R. L. Siddon, “Fast calculation of the exact radiological path
for a three-dimensional CT array,” Med.
Phys. 12, 252–255 (1985).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Weinhardt, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “Time-lapse X-ray phase-contrast microtomography
for in vivo imaging and analysis of morphogenesis,” Nat. Protoc. 9, 294–304 (2014).

[Crossref]
[PubMed]

J. Moosmann, A. Ershov, V. Altapova, T. Baumbach, M. S. Prasad, C. LaBonne, X. Xiao, J. Kashef, and R. Hofmann, “X-ray phase-contrast in vivo microtomography
probes new aspects of Xenopus gastrulation,” Nature 497, 374–377 (2013).

[Crossref]
[PubMed]

L. Reichel and G. Rodriguez, “Old and new parameter choice rules for discrete
ill-posed problems,” Numer. Algorithms 63, 65–87 (2013).

[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.
Express 21, 710–723 (2013).

[Crossref]
[PubMed]

J. Moosmann, R. Hofmann, and T. Baumbach, “Single-distance phase retrieval at large phase
shifts,” Opt. Express 19, 12066–12073 (2011).

[Crossref]
[PubMed]

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

[Crossref]

W. W. Hager and H. Zhang, “A survey of nonlinear conjugate gradient
methods,” Pac. J. Optim. 2, 35–58 (2006).

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

[Crossref]
[PubMed]

T. dos Santos Rolo, A. Ershov, T. van de Kamp, and T. Baumbach, “In vivo X-ray cine-tomography for tracking
morphological dynamics,” Proc. Natl. Acad. Sci.
USA 111, 3921–3926 (2014).

[Crossref]
[PubMed]

T. van de Kamp, P. Vagovič, T. Baumbach, and A. Riedel, “A biological screw in a beetle’s
leg,” Science 333, 52 (2011).

[Crossref]

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

[Crossref]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized
problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

[Crossref]

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

[Crossref]

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for
total variation image reconstruction,” SIAM J.
Imaging Sci. 1, 248–272 (2008).

[Crossref]

Y. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a
strong global convergence property,” SIAM J.
Optimiz. 10, 177–182 (1999).

[Crossref]

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of
discrete ill-posed problems,” SIAM J. Sci.
Comput. 14, 1487–1503 (1993).

[Crossref]

V. A. Morozov, “On the solution of functional equations by the
method of regularization,” “Soviet Math.
Dokl,”, 7, pp. 414–417 (1966.

G. H. Golub, M. Heath, and G. Wahba, “Generalized cross-validation as a method for
choosing a good ridge parameter,” Technometrics 21, 215–223 (1979).

[Crossref]

X. Tai and C. Wu, “Augmented Lagrangian method, dual methods and
split Bregman iteration for ROF model,” in “Scale
Space and Variational Methods in Computer Vision,” (Springer, 2009), pp. 502–513.

[Crossref]

C. Li, W. Yin, and Y. Zhang, “User’s guide for TVAL3: TV minimization by augmented
lagrangian and alternating direction algorithms,” CAAM Report (2009).

C. Li, Compressive Sensing for 3D Data Processing
Tasks: Applications, Models and Algorithms, (PhD
Thesis in Rice University, 2011).

T. Goldstein, B. O’Donoghue, and S. Setzer, “Fast alternating direction optimization
methods,” CAM report pp. 12–35 (2012).

R. Hofmann, A. Schober, J. Moosmann, M. Hertel, S. Hahn, V. Weinhardt, D. Hänschke, L. Helfen, X. Xiao, and T. Baumbach, “Single-distance livecell imaging with
propagation-based X-ray phase contrast,” to be submitted.

A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (Society for Industrial and Applied Mathematics, 2001).

[Crossref]

X. Yang, T. Jejkal, H. Pasic, R. Stotzka, A. Streit, J. van Wezel, and T. dos Santos Rolo, “Data intensive computing of X-ray computed tomography
reconstruction at the LSDF,” in “21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP),” (IEEE, 2013), pp. 86–93.

G. N. Hounsfield, “A method and apparatus for examination of a body by
radiation such as X-ray or gamma radiation,” (1972). Patent Specification 1283915.

The energy dependence of the
complex refractive index can be obtained for a variety of chemical
compounds under http://henke.lbl.gov/optical_constants/getdb2.html .