Abstract

Grating-based phase-contrast is a hot topic in recent years owing to its excellent imaging contrast capability on soft tissues. Although it is compatible with conventional X-ray tubes and applicable in many fields, long scanning time, and high radiation dose obstruct its wider use in clinical and medical fields, especially for computed tomography applications. In this study, we solve this challenge by reducing the projection views and compensating the loss of reconstruction quality through dual-dictionary learning algorithm. The algorithm is implemented in two steps. First, estimated high-quality absorption images are obtained from the first dual-quality dictionary learning, which uses the correspondence between high-quality images and low-quality ones reconstructed from highly under-sampled data. Then, the second absorption-phase dual-modality dictionary learning is adopted to yield both estimated phase and absorption images, resulting in complementary information for both modality images. Afterwards the absorption and phase images are gradually improved in iterative reconstructions. By using SSIM RMSE measurements and visual assessment for enlarged regions of interest, our proposed method can improve the resolution of these two modality images and recover smaller structures, as compared to conventional methods.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

2016 (1)

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

2015 (2)

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

2013 (2)

2012 (3)

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Q. Xu, E. Y. Sidky, X. Pan, M. Stampanoni, P. Modregger, and M. A. Anastasio, “Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography,” Opt. Express 20(10), 10724–10749 (2012).
[Crossref] [PubMed]

Y. Lu, J. Zhao, and G. Wang, “Fair-view image reconstruction with dual dictionaries,” Phys. Med. Biol. 57(1), 173–189 (2012).
[Crossref] [PubMed]

2011 (1)

T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref] [PubMed]

2009 (1)

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” X-Ray Sci. Technol. 14(2), 119–139 (2009).

2008 (1)

G.-H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

2006 (2)

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]

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

2004 (1)

J. A. Tropp, “Greed is Good: Algorithmic Results for Sparse Approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

2003 (2)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys. 30(8), 2169–2179 (2003).
[Crossref] [PubMed]

2002 (2)

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

1999 (1)

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(19), 2912–2914 (1999).
[Crossref]

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

1996 (1)

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

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

1965 (1)

U. Bonse and M. Hart, “AN X‐RAY INTERFEROMETER WITH LONG SEPARATED INTERFERING BEAM PATHS,” Appl. Phys. Lett. 7(4), 99–100 (1965).
[Crossref]

Aharon, M.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Anastasio, M. A.

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Babyn, P.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Baruchel, J.

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(19), 2912–2914 (1999).
[Crossref]

Bech, M.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Bonse, U.

U. Bonse and M. Hart, “AN X‐RAY INTERFEROMETER WITH LONG SEPARATED INTERFERING BEAM PATHS,” Appl. Phys. Lett. 7(4), 99–100 (1965).
[Crossref]

Börner, M.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Brendel, B.

T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref] [PubMed]

Bruckstein, A.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

Bunk, O.

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]

Cao, W.

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Chen, G.-H.

G.-H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Cloetens, P.

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(19), 2912–2914 (1999).
[Crossref]

David, C.

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]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Elad, M.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

El-Gayed, A.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Fehringer, A.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Gao, D.

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

Gmür, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Groso, A.

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

Guigay, J. P.

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(19), 2912–2914 (1999).
[Crossref]

Gureyev, T. E.

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

Hahn, D.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Hart, M.

U. Bonse and M. Hart, “AN X‐RAY INTERFEROMETER WITH LONG SEPARATED INTERFERING BEAM PATHS,” Appl. Phys. Lett. 7(4), 99–100 (1965).
[Crossref]

Hwu, Y.

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

Je, J. H.

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Kajiwara, K.

Kao, C.-M.

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” X-Ray Sci. Technol. 14(2), 119–139 (2009).

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Koehler, T.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Köhler, T.

T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref] [PubMed]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Kou, B.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Lefkimmiatis, S.

Leng, S.

G.-H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Li, J.

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

Liu, H.

X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys. 30(8), 2169–2179 (2003).
[Crossref] [PubMed]

Lu, Y.

Y. Lu, J. Zhao, and G. Wang, “Fair-view image reconstruction with dual dictionaries,” Phys. Med. Biol. 57(1), 173–189 (2012).
[Crossref] [PubMed]

Ludwig, W.

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(19), 2912–2914 (1999).
[Crossref]

Margaritondo, G.

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

Melli, S. A.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Modregger, P.

Mohr, J.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Montgomery, J.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Nilchian, M.

Noda, D.

Noël, P. B.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Nöhammer, B.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Pan, X.

Pettitt, M.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Pfeiffer, F.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

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]

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Pogany, A.

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

Qi, J.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Roessl, E.

T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref] [PubMed]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Schlenker, M.

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(19), 2912–2914 (1999).
[Crossref]

Shen, Y.

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

Sidky, E. Y.

Snead, E.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Solak, H. H.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Song, Y.

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

Stampanoni, M.

Stevenson, A. W.

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

Sun, H.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Sun, J.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Tang, J.

G.-H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Thibault, P.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Tropp, J. A.

J. A. Tropp, “Greed is Good: Algorithmic Results for Sparse Approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

Tsai, W. L.

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

Unser, M.

Van Dyck, D.

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(19), 2912–2914 (1999).
[Crossref]

Van Landuyt, J.

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(19), 2912–2914 (1999).
[Crossref]

Vonesch, C.

Wahid, K. A.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Wang, G.

Y. Lu, J. Zhao, and G. Wang, “Fair-view image reconstruction with dual dictionaries,” Phys. Med. Biol. 57(1), 173–189 (2012).
[Crossref] [PubMed]

Wang, Y.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

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]

Wesolowski, M.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Wilkins, S. W.

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

Wolkowski, B.

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Wu, X.

X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys. 30(8), 2169–2179 (2003).
[Crossref] [PubMed]

Xi, Y.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Xiao, T.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Xu, L. X.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Xu, Q.

Yashiro, W.

Zhao, J.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Y. Lu, J. Zhao, and G. Wang, “Fair-view image reconstruction with dual dictionaries,” Phys. Med. Biol. 57(1), 173–189 (2012).
[Crossref] [PubMed]

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Zhu, Z.

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

Ziegler, E.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[Crossref]

Appl. Phys. Lett. (3)

U. Bonse and M. Hart, “AN X‐RAY INTERFEROMETER WITH LONG SEPARATED INTERFERING BEAM PATHS,” Appl. Phys. Lett. 7(4), 99–100 (1965).
[Crossref]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[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(19), 2912–2914 (1999).
[Crossref]

IEEE Trans. Inf. Theory (1)

J. A. Tropp, “Greed is Good: Algorithmic Results for Sparse Approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

IEEE Trans. Signal Process. (1)

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process. 54(11), 4311–4322 (2006).
[Crossref]

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

Y. Hwu, W. L. Tsai, A. Groso, G. Margaritondo, and J. H. Je, “Coherence-enhanced synchrotron radiology: Simple theory and practical applications,” J. Phys. D Appl. Phys. 35(13), 105–120 (2002).
[Crossref]

J. Synchrotron Radiat. (1)

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat. 19(5), 821–826 (2012).
[Crossref] [PubMed]

Jpn. J. Appl. Phys (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot Interferometry,” Jpn. J. Appl. Phys.  42(7), L866–L868 (2003).

Med. Phys. (3)

X. Wu and H. Liu, “Clinical implementation of x-ray phase-contrast imaging: theoretical foundations and design considerations,” Med. Phys. 30(8), 2169–2179 (2003).
[Crossref] [PubMed]

T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref] [PubMed]

G.-H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Nat. Phys. (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]

Nature (1)

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

Neurocomputing (1)

Y. Shen, J. Li, Z. Zhu, W. Cao, and Y. Song, “Image reconstruction algorithm from compressed sensing measurements by dictionary learning,” Neurocomputing 151, 1153–1162 (2015).
[Crossref]

Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. (1)

S. A. Melli, K. A. Wahid, P. Babyn, J. Montgomery, E. Snead, A. El-Gayed, M. Pettitt, B. Wolkowski, and M. Wesolowski, “A compressed sensing based reconstruction algorithm for synchrotron source propagation-based X-ray phase contrast computed tomography,” Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers. Detect. Assoc. Equip. 806, 307–317 (2016).
[Crossref]

Opt. Express (4)

Phys. Med. Biol. (2)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Y. Lu, J. Zhao, and G. Wang, “Fair-view image reconstruction with dual dictionaries,” Phys. Med. Biol. 57(1), 173–189 (2012).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x‐ray phase contrast microimaging by coherent high‐energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Sci. Rep. (1)

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5(1), 10452 (2015).
[Crossref] [PubMed]

X-Ray Sci. Technol. (1)

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” X-Ray Sci. Technol. 14(2), 119–139 (2009).

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Figures (5)

Fig. 1
Fig. 1 Phase image and absorption image of the mouse paw. (a) phase image, (b) absorption image. Bar: 1mm.
Fig. 2
Fig. 2 SSIM of reconstructed phase images.
Fig. 3
Fig. 3 RMSE of reconstructed phase images.
Fig. 4
Fig. 4 SSIM and RMSE of reconstructed absorption images.
Fig. 5
Fig. 5 Zoomed-in images of region of interest of the mouse paw (a) Reference, (b) Proposed, (c) DRS-TV, (d) FBP, (e) POCS-TV, (f) SIR.

Tables (1)

Tables Icon

Table 1 Experimental parameters for the tomographic scans

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

min D,{ α j } j D α j R j x 2 2 subject to α j 0 ρ,j,
min α j j D α j R j x 2 2 subject to α j 0 ρ,j.
[ D high D low ]=ksvd{[ x high x low ]}.
R j [ x high x low ]=[ D high D low ] α j .
min α j j D low α j R j x low 2 2 subject to α j 0 ρ,j,
x high = ( j R j T R j ) 1 j R j T D high α j .
[ D absorption D phase ]=ksvd{[ x absorption x phase ]}.
min β j j D absorption β j R j x absorption 2 2 subject to β j 0 ρ,j,
x phase est = ( j R j T R j ) 1 j R j T D phase β j .
[ A ] m,n = [ A ] m=t×S+s,n = (2πα) 1/2 I m (α) × ξ a ( 1 ( ξ a ) 2 ) m1/2 × I m1/2 (α 1 ( ξ a ) 2 ),
ζ=s Δ d x n cos(t Δ ϑ ) y n sin(t Δ ϑ ).
min x 1 2 Axb 2 2 +λ Fx 1 .
min x 1 2 Axb 2 2 + λ 1 Fx 1 + λ 2 F(x x est ) 1 .
min x a , x p 1 2 A 1 x a b 1 2 2 +λ F x a 1 + 1 2 A 2 x p b 2 2 2 +λ F x p 1 .
x next = x current A i x current p i A i 2 A i T ,
min x 1 2 Axb 2 2 + λ 1 Fx 1 + λ 2 R(x, x absorption , δ B / μ B ),

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