## Fast iterative reconstruction of differential phase contrast X-ray tomograms |

Optics Express, Vol. 21, Issue 5, pp. 5511-5528 (2013)

http://dx.doi.org/10.1364/OE.21.005511

Enhanced HTML Acrobat PDF (2120 KB)

### Abstract

Differential phase-contrast is a recent technique in the context of X-ray imaging. In order to reduce the specimen’s exposure time, we propose a new iterative algorithm that can achieve the same quality as FBP-type methods, while using substantially fewer angular views. Our approach is based on 1) a novel spline-based discretization of the forward model and 2) an iterative reconstruction algorithm using the alternating direction method of multipliers. Our experimental results on real data suggest that the method allows to reduce the number of required views by at least a factor of four.

© 2013 OSA

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(110.6960) Imaging systems : Tomography

(340.7440) X-ray optics : X-ray imaging

**ToC Category:**

Image Processing

**History**

Original Manuscript: December 20, 2012

Revised Manuscript: January 24, 2013

Manuscript Accepted: January 25, 2013

Published: February 27, 2013

**Virtual Issues**

Vol. 8, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Masih Nilchian, Cédric Vonesch, Peter Modregger, Marco Stampanoni, and Michael Unser, "Fast iterative reconstruction of differential phase contrast X-ray tomograms," Opt. Express **21**, 5511-5528 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-5-5511

Sort: Year | Journal | Reset

### References

- V. Ingal and E. Beliaevskaya, “X-ray plane-wave tomography observation of the phase contrast from a non-crystalline object,” J. Phys. D: Appl. Phys28, 2314–2317 (1995). [CrossRef]
- T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nat.373, 595–598 (1995). [CrossRef]
- D. Chapman, S. Patel, and D. Fuhrman, “Diffraction enhanced X-ray imaging,” Phys., Med. and Bio.42, 2015–2025 (1997). [CrossRef]
- U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6, 155–156 (1965). [CrossRef]
- A. Momose, T. Takeda, Y. itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med2, 473–475 (1996). [CrossRef] [PubMed]
- T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005). [CrossRef] [PubMed]
- A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelekov, “On the possibilities of X-ray phase-contrast microimaging by coherent high-energy synchroton radiation,” Rev. Sci. Instrum.66, 5486–5492 (1997). [CrossRef]
- K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996). [CrossRef] [PubMed]
- S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nat.384, 335–338 (1996). [CrossRef]
- A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jap. Jour. of Appl. Phys.42, L866–L868 (2003). [CrossRef]
- F. Pfieffer, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Inst. and Meth. in Phys. Res.580.2, 925–928 (2007). [CrossRef]
- M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Inves. radio.46, 801–806 (2011). [CrossRef]
- M. Nilchian and M. Unser, “Differential phase-contrast X-ray computed tomography: From model discretization to image reconstruction,” Proc. of the Ninth IEEE Inter. Symp. on Biomed. Imag.: From Nano to Macro (ISBI’12), 90–93 (2012).
- M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Trans. Imag. Proc.20, 681–695 (2011). [CrossRef]
- S. Ramani and J. A. Fessler, “A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction,” IEEE Trans. Med. Imag.31.3, 677–688 (2012). [CrossRef]
- Z. Qi, J. Zambelli, N. Bevins, and G. Chen, “A novel method to reduce data acquisition time in differential phase contrast computed tomography using compressed sensing,” Proc. of SPIE7258, 4A1–8 (2009).
- T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. phys.38, 4542–4545 (2011). [CrossRef]
- 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. Express20, 10724–10749 (2012). [CrossRef] [PubMed]
- M. Unser, “Sampling–50 years after Shannon,” Proc. IEEE88, 254104–1–3 (2000). [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]
- A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006). [CrossRef]
- F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron phase imaging and tomography,” Phys. Rev. Lett.96, 215505-1–4 (2006). [CrossRef]
- F. Natterer, The Mathematics of Computed Tomography (John Wiley and sons, 1986).
- H. Meijering, J. Niessen, and A. Viergever, “Quantitative evaluation of convolution-based methods for medical image interpolation,” Med. Imag. Anal.5, 111–126 (2001). [CrossRef]
- A. Entezari, M. Nilchian, and M. Unser, “A box spline calculus for the discretization of computed tomography reconstruction problems,” IEEE Trans. Med. Imag.31, 1532 –1541 (2012). [CrossRef]
- P. Thvenaz, T. Blu, and M. Unser, “Interpolation revisited [medical images application],” IEEE Trans. Med. Imag.19.7, 739–758 (2000). [CrossRef]
- Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM Jour. on Imag. Sci.1, 248–272 (2008). [CrossRef]
- T. Goldstein and S. Osher, “The split bregman method for l1-regularized problems,” SIAM Jour. on Imag. Sci.2, 323–343 (2009). [CrossRef]
- M. Ng, P. Weiss, and X. Yuan, “Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods,” SIAM Jour. on Sci. Comp.32, 2710–2736 (2010). [CrossRef]
- B. Vandeghinste, B. Goossens, J. De Beenhouwer, A. Pizurica, W. Philips, S. Vandenberghe, and S. Staelens, “Split-bregman-based sparse-view CT reconstruction,” in “Fully 3D 2011 proc.,” 431–434 (2011).
- I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.57, 1413–1457 (2004). [CrossRef]
- A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM Imag. Sci.2, 183–202 (2009). [CrossRef]
- Z. Wang and A. Bovik, “A universal image quality index,” IEEE Sig. Proc. Lett.9, 81 –84 (2002). [CrossRef]
- Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Imag. Proc.13, 600–612 (2004). [CrossRef]
- S. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” Sync. Rad.16, 562–572 (2009). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.