An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval

NI Wen-lei; ZHOU Tie

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(1): 93-103

NI Wen-lei, ZHOU Tie. An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval[J]. Applied Mathematics and Mechanics, 2008, 29(1): 93-103.

Citation:

NI Wen-lei, ZHOU Tie. An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval[J]. Applied Mathematics and Mechanics, 2008, 29(1): 93-103.

Citation:

NI Wen-lei, ZHOU Tie. An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval[J]. Applied Mathematics and Mechanics, 2008, 29(1): 93-103.

PDF( 455 KB)

An Algorithm for Phase Contrast X-ray Tomography Based on the Nonlinear Phase Retrieval

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

Received Date: 2007-08-03
Rev Recd Date: 2007-12-17
Publish Date: 2008-01-15

Abstract

Abstract

A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to beill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, it can be seen that the new algorithm is not limited to be only efficient for the data measured in the nea-rfield of the Fresnel region and thus it has a broader validity range.
- phase contrast tomography,
- holographic measurement,
- phaseretrieval

FullText(HTML)

References(24)

References

[1]	Lewis R A.Medical phase contrast X-ray imaging: Current status and future prospects[J].Physics in Medicine and Biology,2004,49(16):3573-3583. doi: 10.1088/0031-9155/49/16/005
[2]	Suzuki Y,Yagi N,Uesugi K.X-ray refraction-enhanced imaging and a method for phase retrieval for a simple object[J].Journal of Synchrotron Radiation,2002,9(3):160-165. doi: 10.1107/S090904950200554X
[3]	Spanne P ,Raven C,Snigireva I,et al.In-line holography and phase-contrast microtomography with high energy X-rays[J].Physics in Medicines and Biology,1999,44(3):741-749. doi: 10.1088/0031-9155/44/3/016
[4]	Arfelli F, Assante M,Bonvicini V,et al.Low-dose phase contrast X-ray medical imaging[J].Physics in Medicine and Biology,1998,43(10):2845-2852. doi: 10.1088/0031-9155/43/10/013
[5]	Ingal V N, Beliaevskaya E A,Brianskaya A P,et al.Phase mammography-anew technique for breast investigation[J].Physics in Medicine and Biology,1998,43(9):2555-2567. doi: 10.1088/0031-9155/43/9/009
[6]	Ando M， Hosoya S.An attempt at X-ray phase-contrast microscopy[A].In:Shinoda G, Kohra K,Ichinokawa T, Eds.Proceedings of the 6th International Conference of X Ray Optics and Microanalysis[C].Tokyo:Univerisity of Tokyo Press, 1972, 63-68.
[7]	Momose A. Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer[J].Nuclear Instruments and Methods in Physics Research A,1995,352(3):622-628. doi: 10.1016/0168-9002(95)90017-9
[8]	Chapman D, Thomlinson W,Johnston R E,et al.Diffraction enhanced X-ray imaging[J].Physics in Medicine and Biology, 1997,42(11):2015-2025. doi: 10.1088/0031-9155/42/11/001
[9]	Dilmanian F A, Zhong Z, Ren B,et al.Computed tomography of X-ray index of refraction using the diffraction enhanced imaging method[J].Physics in Medicine and Biology,2000,45(4):933-946. doi: 10.1088/0031-9155/45/4/309
[10]	Pfeiffer F,Weitkamp T,Bunk O,et al.Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources[J].Nature Physics,2006,2(4):258-261. doi: 10.1038/nphys265
[11]	Momose A,Yashiro W,Takeda Y,et al.Phase tomography by X-ray talbot interferometry for biological imaging[J].Japanese of Applied Physics,2006,45(6A):5254-5262. doi: 10.1143/JJAP.45.5254
[12]	Gureyev T E, Nugent K A. Rapid quantitative phase imaging using the transport of intensity equation[J].Optics Communications,1997,133(1):339-346. doi: 10.1016/S0030-4018(96)00454-3
[13]	Barty A, Nugent K A, Roberts A,et al.Quantitative phase tomography[J].Optics Communication,2000,175(4):329-336. doi: 10.1016/S0030-4018(99)00726-9
[14]	Gureyev T E, Raven C,Snigirev A,et al.Hard X-ray quantitative non-interferometric phase-contrast microscopy[J].Journal of Physics D: Applied Physics,1999,32(5):563-567. doi: 10.1088/0022-3727/32/5/010
[15]	Jonas P, Louis A K. Phase contrast tomography using holographic measurements[J].Inverse Problems,2004,20(1):75-102. doi: 10.1088/0266-5611/20/1/005
[16]	Bronnikov A V.Theory of quantitative phase-contrast computed tomography[J].Journal of the Optical Society of America A,2002,19(3):472-480. doi: 10.1364/JOSAA.19.000472
[17]	Born M,Wolf E.Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light[M].Cambridge:Cambridge University Press, 2001.
[18]	Gureyev T E, Wilkins S W.On X-ray phase imaging with a point source[J].Journal of the Optical Society of America A,1998,15(3):579-585. doi: 10.1364/JOSAA.15.000579
[19]	Als-Nielsen J, McMorrow D.Elements of Modern X-Ray Physics[M].New York:Wiley, 2001.
[20]	Wu X,Deans A E,Liu H.X-ray diagnostic techniques[A].In:Vo-Dinh T，Ed.Biomedical Photonics Handbook[C].Tampa: CRC Press,2003,26.1-26.34.
[21]	Gureyev T E, Pogany A, Paganin D M,et al.Linear algorithms for phase retrieval in the Fresnel region[J].Optics Communications,2004,231(1/6):53-70. doi: 10.1016/j.optcom.2003.12.020
[22]	Huntley J M.Noise-immune phase unwrapping algorithm[J].Applied Optics,1989,28(15):3268-3270. doi: 10.1364/AO.28.003268
[23]	Kak A C,Slaney M.Principles of Computerized Tomographic Imaging[M].New York:IEEE Press,1988.
[24]	Kaipio J, Somersalo E.Statistical and Computational Inverse Problems[M].New York:Springer, 2005.