Abstract

Edge-illumination X-ray phase-contrast tomography (EIXPCT) is an emerging technique that enables practical phase-contrast imaging with laboratory-based X-ray sources. A joint reconstruction method was proposed for reconstructing EIXPCT images, enabling novel flexible data-acquisition designs. However, only limited efforts have been devoted to optimizing data-acquisition designs for use with the joint reconstruction method. In this study, several promising designs are introduced, such as the constant aperture position (CAP) strategy and the alternating aperture position (AAP) strategy covering different angular ranges. In computer-simulation studies, these designs are analyzed and compared. Experimental data are employed to test the designs in real-world applications. All candidate designs are also compared for their implementation complexity. The tradeoff between data-acquisition time and image quality is discussed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]

2018 (1)

Y. Chen and M. A. Anastasio, “Properties of a joint reconstruction method for edge-illumination X-ray phase-contrast tomography,” Sens. Imaging 19(1), 7 (2018).
[Crossref]

2017 (4)

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

Y. Chen, H. Guan, C. K. Hagen, A. Olivo, and M. A. Anastasio, “Single-shot edge illumination X-ray phase-contrast tomography enabled by joint image reconstruction,” Opt. Lett. 42(3), 619–622 (2017).
[Crossref]

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

C. K. Hagen, P. C. Diemoz, and A. Olivo, “On the relative performance of edge illumination X-ray phase-contrast CT and conventional, attenuation-based CT,” Med. Phys. 44(5), 1876–1885 (2017).
[Crossref]

2016 (3)

C. K. Hagen, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Reverse projection retrieval in edge illumination X-ray phase contrast computed tomography,” J. Phys. D: Appl. Phys. 49(25), 255501 (2016).
[Crossref]

M. Endrizzi, A. Astolfo, F. A. Vittoria, T. P. Millard, and A. Olivo, “Asymmetric masks for laboratory-based X-ray phase-contrast imaging with edge illumination,” Sci. Rep. 6(1), 25466 (2016).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

2015 (1)

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

2014 (5)

M. Das and Z. Liang, “Spectral X-ray phase contrast imaging for single-shot retrieval of absorption, phase, and differential-phase imagery,” Opt. Lett. 39(21), 6343–6346 (2014).
[Crossref]

P. C. Diemoz and A. Olivo, “On the origin of contrast in edge illumination X-ray phase-contrast imaging,” Opt. Express 22(23), 28199–28214 (2014).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

A. Ruhlandt, M. Krenkel, M. Bartels, and T. Salditt, “Three-dimensional phase retrieval in propagation-based phase-contrast imaging,” Phys. Rev. A 89(3), 033847 (2014).
[Crossref]

A. Sawatzky, Q. Xu, C. O. Schirra, and M. A. Anastasio, “Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT,” IEEE T. Med. Imaging 33(8), 1657–1668 (2014).
[Crossref]

2013 (1)

2012 (1)

2010 (2)

P. R. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express 18(5), 4103–4117 (2010).
[Crossref]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

2009 (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. on Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

2007 (3)

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref]

A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

2002 (1)

D. Stout, “Creating a whole body digital mouse atlas with PET, CT and cryosection images,” Mol. Imaging Biol. 4(1), 27–33 (2002).
[Crossref]

1996 (1)

S. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

1995 (1)

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Anastasio, M. A.

Y. Chen and M. A. Anastasio, “Properties of a joint reconstruction method for edge-illumination X-ray phase-contrast tomography,” Sens. Imaging 19(1), 7 (2018).
[Crossref]

Y. Chen, H. Guan, C. K. Hagen, A. Olivo, and M. A. Anastasio, “Single-shot edge illumination X-ray phase-contrast tomography enabled by joint image reconstruction,” Opt. Lett. 42(3), 619–622 (2017).
[Crossref]

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

A. Sawatzky, Q. Xu, C. O. Schirra, and M. A. Anastasio, “Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT,” IEEE T. Med. Imaging 33(8), 1657–1668 (2014).
[Crossref]

Y. Chen, W. Zhou, and M. A. Anastasio, “Joint-reconstruction-enabled data acquisition design for single-shot edge-illumination X-ray phase-contrast tomography,” in Medical Imaging 2018: Physics of Medical Imaging, vol. 10573 (International Society for Optics and Photonics, 2018), p. 1057322.

Arfelli, F.

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Astolfo, A.

M. Endrizzi, A. Astolfo, F. A. Vittoria, T. P. Millard, and A. Olivo, “Asymmetric masks for laboratory-based X-ray phase-contrast imaging with edge illumination,” Sci. Rep. 6(1), 25466 (2016).
[Crossref]

Bartels, M.

A. Ruhlandt, M. Krenkel, M. Bartels, and T. Salditt, “Three-dimensional phase retrieval in propagation-based phase-contrast imaging,” Phys. Rev. A 89(3), 033847 (2014).
[Crossref]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. on Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Bellazzini, R.

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Bravin, A.

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

P. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express 20(3), 2789–2805 (2012).
[Crossref]

Brun, E.

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

Bunk, O.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Chatziioannou, A. F.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[Crossref]

Chen, Y.

Y. Chen and M. A. Anastasio, “Properties of a joint reconstruction method for edge-illumination X-ray phase-contrast tomography,” Sens. Imaging 19(1), 7 (2018).
[Crossref]

Y. Chen, H. Guan, C. K. Hagen, A. Olivo, and M. A. Anastasio, “Single-shot edge illumination X-ray phase-contrast tomography enabled by joint image reconstruction,” Opt. Lett. 42(3), 619–622 (2017).
[Crossref]

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

Y. Chen, W. Zhou, and M. A. Anastasio, “Joint-reconstruction-enabled data acquisition design for single-shot edge-illumination X-ray phase-contrast tomography,” in Medical Imaging 2018: Physics of Medical Imaging, vol. 10573 (International Society for Optics and Photonics, 2018), p. 1057322.

Coan, P.

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

P. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express 20(3), 2789–2805 (2012).
[Crossref]

Das, M.

David, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Davis, T.

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

De Coppi, P.

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

Diemoz, P.

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

P. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express 20(3), 2789–2805 (2012).
[Crossref]

Diemoz, P. C.

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

C. K. Hagen, P. C. Diemoz, and A. Olivo, “On the relative performance of edge illumination X-ray phase-contrast CT and conventional, attenuation-based CT,” Med. Phys. 44(5), 1876–1885 (2017).
[Crossref]

C. K. Hagen, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Reverse projection retrieval in edge illumination X-ray phase contrast computed tomography,” J. Phys. D: Appl. Phys. 49(25), 255501 (2016).
[Crossref]

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

P. C. Diemoz and A. Olivo, “On the origin of contrast in edge illumination X-ray phase-contrast imaging,” Opt. Express 22(23), 28199–28214 (2014).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Dogdas, B.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[Crossref]

Dreoosi, D.

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Endrizzi, M.

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

C. K. Hagen, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Reverse projection retrieval in edge illumination X-ray phase contrast computed tomography,” J. Phys. D: Appl. Phys. 49(25), 255501 (2016).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

M. Endrizzi, A. Astolfo, F. A. Vittoria, T. P. Millard, and A. Olivo, “Asymmetric masks for laboratory-based X-ray phase-contrast imaging with edge illumination,” Sci. Rep. 6(1), 25466 (2016).
[Crossref]

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Gao, D.

S. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Grünzweig, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref]

Guan, H.

Gureyev, T.

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Gureyev, T. E.

S. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Hagen, C.

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

Hagen, C. K.

Y. Chen, H. Guan, C. K. Hagen, A. Olivo, and M. A. Anastasio, “Single-shot edge illumination X-ray phase-contrast tomography enabled by joint image reconstruction,” Opt. Lett. 42(3), 619–622 (2017).
[Crossref]

C. K. Hagen, P. C. Diemoz, and A. Olivo, “On the relative performance of edge illumination X-ray phase-contrast CT and conventional, attenuation-based CT,” Med. Phys. 44(5), 1876–1885 (2017).
[Crossref]

C. K. Hagen, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Reverse projection retrieval in edge illumination X-ray phase contrast computed tomography,” J. Phys. D: Appl. Phys. 49(25), 255501 (2016).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

P. R. Munro, C. K. Hagen, M. B. Szafraniec, and A. Olivo, “A simplified approach to quantitative coded aperture X-ray phase imaging,” Opt. Express 21(9), 11187–11201 (2013).
[Crossref]

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Hubbell, J. H.

J. H. Hubbell and S. M. Seltzer, “Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z= 1 to 92 and 48 additional substances of dosimetric interest,” Tech. rep., National Inst. of Standards and Technology-PL, Gaithersburg, MD (United States). Ionizing Radiation Div. (1995).

Ignatyev, K.

Kottler, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref]

Krenkel, M.

A. Ruhlandt, M. Krenkel, M. Bartels, and T. Salditt, “Three-dimensional phase retrieval in propagation-based phase-contrast imaging,” Phys. Rev. A 89(3), 033847 (2014).
[Crossref]

Leahy, R. M.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[Crossref]

Liang, Z.

Liu, X.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Liu, Y.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Longo, R.

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Lopez, F. C.

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Louise Jones, J.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

Marone, F.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

McDonald, S. A.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Millard, T. P.

M. Endrizzi, A. Astolfo, F. A. Vittoria, T. P. Millard, and A. Olivo, “Asymmetric masks for laboratory-based X-ray phase-contrast imaging with edge illumination,” Sci. Rep. 6(1), 25466 (2016).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

Minuti, M.

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

Munro, P. R.

Olivo, A.

C. K. Hagen, P. C. Diemoz, and A. Olivo, “On the relative performance of edge illumination X-ray phase-contrast CT and conventional, attenuation-based CT,” Med. Phys. 44(5), 1876–1885 (2017).
[Crossref]

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

Y. Chen, H. Guan, C. K. Hagen, A. Olivo, and M. A. Anastasio, “Single-shot edge illumination X-ray phase-contrast tomography enabled by joint image reconstruction,” Opt. Lett. 42(3), 619–622 (2017).
[Crossref]

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

M. Endrizzi, A. Astolfo, F. A. Vittoria, T. P. Millard, and A. Olivo, “Asymmetric masks for laboratory-based X-ray phase-contrast imaging with edge illumination,” Sci. Rep. 6(1), 25466 (2016).
[Crossref]

C. K. Hagen, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Reverse projection retrieval in edge illumination X-ray phase contrast computed tomography,” J. Phys. D: Appl. Phys. 49(25), 255501 (2016).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

P. C. Diemoz and A. Olivo, “On the origin of contrast in edge illumination X-ray phase-contrast imaging,” Opt. Express 22(23), 28199–28214 (2014).
[Crossref]

P. R. Munro, C. K. Hagen, M. B. Szafraniec, and A. Olivo, “A simplified approach to quantitative coded aperture X-ray phase imaging,” Opt. Express 21(9), 11187–11201 (2013).
[Crossref]

P. R. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express 18(5), 4103–4117 (2010).
[Crossref]

A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

A. Olivo and R. D. Speller, “A novel X-ray imaging technique based on coded apertures making phase contrast imaging feasible with conventional sources,” in 2008 IEEE Nuclear Science Symposium Conference Record, (IEEE, 2008), pp. 1447–1450.

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Pfeiffer, F.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Pogany, A.

S. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

Rau, C.

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

Rigon, L.

C. K. Hagen, P. C. Diemoz, M. Endrizzi, L. Rigon, D. Dreoosi, F. Arfelli, F. C. Lopez, R. Longo, and A. Olivo, “Quantitative edge illumination X-ray phase contrast tomography,” in Developments in X-Ray Tomography IX, vol. 9212 (International Society for Optics and Photonics, 2014), p. 921205.

Robinson, I. K.

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

Ruhlandt, A.

A. Ruhlandt, M. Krenkel, M. Bartels, and T. Salditt, “Three-dimensional phase retrieval in propagation-based phase-contrast imaging,” Phys. Rev. A 89(3), 033847 (2014).
[Crossref]

Salditt, T.

A. Ruhlandt, M. Krenkel, M. Bartels, and T. Salditt, “Three-dimensional phase retrieval in propagation-based phase-contrast imaging,” Phys. Rev. A 89(3), 033847 (2014).
[Crossref]

Sawatzky, A.

A. Sawatzky, Q. Xu, C. O. Schirra, and M. A. Anastasio, “Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT,” IEEE T. Med. Imaging 33(8), 1657–1668 (2014).
[Crossref]

Schirra, C. O.

A. Sawatzky, Q. Xu, C. O. Schirra, and M. A. Anastasio, “Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT,” IEEE T. Med. Imaging 33(8), 1657–1668 (2014).
[Crossref]

Seltzer, S. M.

J. H. Hubbell and S. M. Seltzer, “Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z= 1 to 92 and 48 additional substances of dosimetric interest,” Tech. rep., National Inst. of Standards and Technology-PL, Gaithersburg, MD (United States). Ionizing Radiation Div. (1995).

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Speller, R.

A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Speller, R. D.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

P. R. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express 18(5), 4103–4117 (2010).
[Crossref]

A. Olivo and R. D. Speller, “A novel X-ray imaging technique based on coded apertures making phase contrast imaging feasible with conventional sources,” in 2008 IEEE Nuclear Science Symposium Conference Record, (IEEE, 2008), pp. 1447–1450.

Stampanoni, M.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Stevenson, A.

S. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Stout, D.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[Crossref]

D. Stout, “Creating a whole body digital mouse atlas with PET, CT and cryosection images,” Mol. Imaging Biol. 4(1), 27–33 (2002).
[Crossref]

Szafraniec, M. B.

Teboulle, M.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. on Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Urbani, L.

P. Diemoz, C. Hagen, M. Endrizzi, M. Minuti, R. Bellazzini, L. Urbani, P. De Coppi, and A. Olivo, “Single-shot X-ray phase-contrast computed tomography with nonmicrofocal laboratory sources,” Phys. Rev. Appl. 7(4), 044029 (2017).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

Vittoria, F.

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

Vittoria, F. A.

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

M. Endrizzi, A. Astolfo, F. A. Vittoria, T. P. Millard, and A. Olivo, “Asymmetric masks for laboratory-based X-ray phase-contrast imaging with edge illumination,” Sci. Rep. 6(1), 25466 (2016).
[Crossref]

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

Wagner, U. H.

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

Wang, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Wilkins, S.

S. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[Crossref]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Wu, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Xu, Q.

A. Sawatzky, Q. Xu, C. O. Schirra, and M. A. Anastasio, “Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT,” IEEE T. Med. Imaging 33(8), 1657–1668 (2014).
[Crossref]

Zamir, A.

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination X-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref]

Zhang, K.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Zhou, W.

Y. Chen, W. Zhou, and M. A. Anastasio, “Joint-reconstruction-enabled data acquisition design for single-shot edge-illumination X-ray phase-contrast tomography,” in Medical Imaging 2018: Physics of Medical Imaging, vol. 10573 (International Society for Optics and Photonics, 2018), p. 1057322.

Zhu, P.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. 107(31), 13576–13581 (2010).
[Crossref]

Appl. Phys. Lett. (2)

A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. Louise Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104(2), 024106 (2014).
[Crossref]

IEEE T. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004).
[Crossref]

IEEE T. Med. Imaging (1)

A. Sawatzky, Q. Xu, C. O. Schirra, and M. A. Anastasio, “Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT,” IEEE T. Med. Imaging 33(8), 1657–1668 (2014).
[Crossref]

J. Med. Imag. (1)

A. Zamir, C. Hagen, P. C. Diemoz, M. Endrizzi, F. Vittoria, Y. Chen, M. A. Anastasio, and A. Olivo, “Recent advances in edge illumination X-ray phase-contrast tomography,” J. Med. Imag. 4(04), 1 (2017).
[Crossref]

J. Phys. D: Appl. Phys. (1)

C. K. Hagen, M. Endrizzi, P. C. Diemoz, and A. Olivo, “Reverse projection retrieval in edge illumination X-ray phase contrast computed tomography,” J. Phys. D: Appl. Phys. 49(25), 255501 (2016).
[Crossref]

J. Synchrotron Radiat. (1)

P. C. Diemoz, F. A. Vittoria, C. K. Hagen, M. Endrizzi, P. Coan, E. Brun, U. H. Wagner, C. Rau, I. K. Robinson, and A. Bravin, “Single-image phase retrieval using an edge illumination X-ray phase-contrast imaging setup,” J. Synchrotron Radiat. 22(4), 1072–1077 (2015).
[Crossref]

Med. Phys. (1)

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Figures (10)

Fig. 1.
Fig. 1. Schematic of the experimental setup. $A_1$ is the sample mask and is placed before the sample. $A_2$ is the detector mask and is placed immediately before the detector, with a pixel size $P$ . S is the X-ray source. The distance between the source and $A_1$ is denoted as $l_{so}$ , and the distance between $A_1$ and the detector is denoted as $l_{od}$ .
Fig. 2.
Fig. 2. Different mask displacement strategies: (1) CVN strategy, (2) AAP strategy, (3) PCAP strategy, (4) CAP strategy. Each asterisk indicates one image acquired at position 1 or position 2 at the specified tomographic view angle.
Fig. 3.
Fig. 3. The phantoms for (a) (c) absorption distributions and (b) (d) refractive index decrement distributions. (a) and (b) correspond to the geometry phantom; (c) and (d) correspond to the digimouse phantom.
Fig. 4.
Fig. 4. The reconstructed estimates of $\boldsymbol \delta$ for four different mask displacement strategies (columns) with different angular ranges (rows). From left to right, the mask position is changed less and less frequently, while the five rows correspond to 180°, 225°, 270°, 315°, and 360°, respectively. All images are displayed in the same gray-scale window. The panel at the bottom-right corner for each reconstructed image is a gray-scale-adjusted view of a uniform region in the reconstructed object, so that fluctuations in intensity can be better visualized. The image quality is higher when the angular range is larger or the masks are changed more frequently. Increasing angular range would increase dose, while moving the mask would not.
Fig. 5.
Fig. 5. The MSE (top row) and SSIM (bottom row) for the reconstructed refractive index decrement distribution $\boldsymbol \delta$ and absorption distribution $\boldsymbol \beta$ for data-acquisition designs using different mask displacement strategies and tomographic angular scanning ranges.
Fig. 6.
Fig. 6. (a) Single-channel reconstructed estimates of $\boldsymbol \beta$ when imperfect values of $\boldsymbol \delta$ are assumed. The first image shows the imperfect assigned values for $\boldsymbol \delta$ . The other three images show the reconstructed $\boldsymbol \beta$ images. Each corresponds to a data-acquisition design and a specific assigned $\boldsymbol \delta$ . (b) Single-channel reconstructed estimates of $\boldsymbol \delta$ when imperfect values of $\boldsymbol \beta$ are assumed. The first image shows the imperfect assigned values for $\boldsymbol \beta$ . The other three images shows the reconstructed $\boldsymbol \delta$ images. Each corresponds to a data-acquisition design and a specific assigned $\boldsymbol \beta$ .
Fig. 7.
Fig. 7. The gradient with respect to $\boldsymbol \delta$ when $\boldsymbol \delta =0$ and different values are assigned for $\boldsymbol \beta$ : the first row shows when $\boldsymbol \beta =0$ ; the second row shows $\boldsymbol \beta$ being the noisy vector defined in Sec.3.2.3.
Fig. 8.
Fig. 8. The bar region (a, b) and circle region (c, d) of the reconstructed $\boldsymbol \beta$ (a, c) and $\boldsymbol \delta$ (b, d) image of the analytical geometric phantom for the AAP( $2\pi$ ) design with selected regularization parameters from Table 1. From left to right, the regularization parameter for $\boldsymbol \beta$ is increasing. From top to bottom, the regularization parameter for $\boldsymbol \delta$ is increasing.
Fig. 9.
Fig. 9. The bar region (a) and the circle region (b) of the reconstructed absorption distribution (top) and refractive index decrement distribution (bottom) of the analytical geometric phantom for the CAP( $2\pi$ ), AAP( $2\pi$ ), and AAP( $1\pi$ ) designs (from left to right), with an optimal regularization parameter. (c) The averaged profile of the bar region of the reconstructed absorption distribution (left) and refractive index decrement distribution (right) of the analytical geometric phantom for the CAP( $2\pi$ ), AAP( $2\pi$ ), and AAP( $1\pi$ ) designs, with an optimal regularization parameter.
Fig. 10.
Fig. 10. The reconstructed absorption (first row) and refractive index decrement (second row) distributions using three data-acquisition designs. The third row shows a zoomed-in region of the reconstructed chalk section with varying data-acquisition designs.

Tables (3)

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Table 1. Candidate regularization parameters. In Fig. 8, the reconstructed images are only shown for underlined parameters.

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Table 2. MSEs for reconstructed images with the optimal regularization parameters

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Table 3. A comparison of the three single-shot methods (in the table, V is the number of views obtained for π angular range)

Equations (9)

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H θ , y r ( β ( x , y ) ) = L ( y r , θ ) β ( x , y ) d x r ,
D θ , y r ( δ ( x , y ) ) = y r H θ , y r ( δ ( x , y ) ) = y r L ( y r , θ ) δ ( x , y ) d x r ,
I θ , y r ( β , δ ) = exp ( 4 π λ H θ , y r ( β ) ) [ I T C ( Δ ξ θ ) l o d M I T C ( Δ ξ θ ) D θ , y r ( δ ) ] ,
[ I ( β , δ ) ] k = exp ( 4 π λ [ H β ] k ) [ I T C [ Δ ξ ] i l o d M I T C [ Δ ξ ] i [ D δ ] k ] .
( β ~ , δ ~ ) = arg min β 0 , δ 0 f ( β , δ ) = arg min β 0 , δ 0 | | I m I ( β , δ ) | | 2 + R ( β , δ ) ,
R ( β , δ ) = α 1 R T V ( β ) + α 2 R T V ( δ ) .
θ a = N Δ θ .
β ~ = arg min β 0 f ( β , δ ) = arg min β 0 | | I m I ( β , δ ) | | 2 + α 1 R T V ( β ) ,
δ ~ = arg min δ 0 f ( β , δ ) = arg min δ 0 | | I m I ( β , δ ) | | 2 + α 2 R T V ( δ ) .

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