基于卡通纹理模型的相位恢复算法

练秋生; 赵晓蕊; 石保顺; 陈书贞

doi:10.11999/JEIT151156

基于卡通纹理模型的相位恢复算法

doi: 10.11999/JEIT151156

基金项目:

国家自然科学基金(61471313)，河北省自然科学基金(F2014203076)

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- 被引次数: 0
出版历程
- 收稿日期: 2015-10-16
- 修回日期: 2016-02-25
- 刊出日期: 2016-08-19

Phase Retrieval Algorithm Based on Cartoon-texture Model

Funds:

The National Natural Science Foundation of China (61471313), The Natural Science Foundation of Hebei Province (F2014203076)

摘要

摘要: 相位恢复是指仅利用图像的傅里叶幅值对原始图像进行恢复。由于傅里叶幅值中包含的信息量较少，当图像的过采样率相对较低时，传统的相位恢复算法无法实现图像的有效重构。因此如何利用合适的先验知识来提高图像重构质量是相位恢复的一个关键问题。该文将卡通-纹理模型用于相位恢复，利用全变差(TV)和双树复数小波(DTCWT)两种稀疏表示方法将图像分解为卡通成分和纹理成分，并提出了基于交替方向乘子法(ADMM)的有效求解算法。实验结果表明，该算法能有效提高图像重构质量。
- 图像处理 /
- 相位恢复 /
- 卡通-纹理模型 /
- 全变差 /
- 双树复数小波
Abstract: Phase retrieval is an issue that tries to recover an image from its Fourier magnitude measurements. Since the Fourier magnitude measurements contain less information, the traditional phase retrieval algorithms can not reconstruct the image efficiently under the scenario that the oversampling ratio is relatively low. Therefore, how to use the suitable image priors to improve the reconstruction quality of the image is the key issue. In this paper, the cartoon-texture model is utilized for phase retrieval algorithm. Two sparse representation methods including both Total Variation (TV) and Dual-Tree Complex Wavelet Transform (DTCWT) are exploited to decompose the image into two parts, namely the cartoon component and the texture component. Moreover, Alternating Direction Method of Multipliers (ADMM) is exploited to solve the corresponding problem. The experimental results show that the proposed algorithm can effectively improve the quality of image reconstruction.
- Image processing /
- Phase retrieval /
- Cartoon-texture model /
- Total Variation (TV) /
- Dual-Tree Complex Wavelet Transform (DTCWT)

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参考文献(30)

SHECHTMAN Y, ELDAR Y C, COHEN O, et al. Phase retrieval with application to optical imaging: a contemporary overview[J]. IEEE Signal Processing Magazine, 2015, 32(3): 87-109. doi: 10.1109/MSP.2014.2352673.

WANG Xiaogang, CHEN Wen, and CHEN Xudong. Optical encryption and authentication based on phase retrieval and sparsity constraints[J]. IEEE Photonics Journal, 2015, 7(2): 1-10. doi: 10.1109/JPHOT.2015.2412936.

ELDAR Y C, SIDORENKO P, MIXON D G, et al. Sparse phase retrieval from short-time Fourier measurements[J]. IEEE Signal Processing Letters, 2015, 22(5): 638-642. doi: 10.1109/LSP.2014.2364225.

戎路, 王大勇, 王云新, 等. 同轴数字全息中的相位恢复算法[J]. 中国激光, 2014, 41(2): 55-64. doi: 10.3788/cj1201441. 0209006.

RONG Lu, WANG Dayong, WANG Yunxin, et al. Phase retrieval methods in in-line digital holography[J].Chinese Journal of Lasers, 2014, 41(2): 55-64. doi: 10.3788/cj1201441. 0209006.

MIAO J, SAYRE D, and CHAPMAN H N. Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects[J]. Journal of the Optical Society of America A, 1998, 15(6): 1662-1669. doi: 10.1364/JOSAA.15.001662.

GERCHBERG R W and SAXTON W O. A practical algorithm for the determination of phase from image and diffraction plane pictures[J]. Optik, 1972, 35(2): 237-250.

杨国桢, 顾本源. 光学系统中振幅和相位的恢复问题[J]. 物理学报, 1981, 30(3): 410-413.

YANG Guozhen and GU Benyuan. On the amplitude-phase retrieval problem in optical systems[J]. Acta Physica Sinica, 1981, 30(3): 410-413.

FIENUP J R. Phase retrieval algorithms: a comparison[J]. Applied Optics, 1982, 21(15): 2758-2769. doi: 10.1364/A0.21. 002758.

ELSER V. Phase retrieval by iterated projections[J]. Journal of the Optical Society of America A, 2003, 20(1): 40-55. doi: 10.1364/JOSAA.20.000040.

程鸿, 章权兵, 韦穗. 基于整体变分的相位恢复[J]. 中国图象图形学报, 2010, 15(10): 1425-1429. doi: 10.11834/jig. 20101007.

CHENG Hong, ZHANG Quanbing, and WEI Sui. Phase retrieval based on total variation[J]. Journal of Image and Graphics, 2010, 15(10): 1425-1429. doi: 10.11834/jig. 20101007.

杨振亚, 郑楚君. 基于压缩传感的纯相位物体相位恢复[J]. 物理学报, 2013, 62(10): 104203. doi: 10.7498/aps.62.104203.

YANG Zhenya and ZHENG Chujun. Phase retrieval of pure phase object based on compressed sensing[J]. Acta Physica Sinica, 2013, 62(10): 104203. doi: 10.7498/aps.62.104203.

CHAMBOLLE A. An algorithm for total variation minimization and applications[J]. Journal of Mathematical Imaging and Vision, 2004, 20(1): 89-97. doi: 10.1023/ B:JMIV.0000011325.36760.1e.

SHECHTMAN Y, BECK A, and ELDAR Y C. GESPAR: Efficient phase retrieval of sparse signals[J]. IEEE Transactions on Signal Processing, 2014, 62(4): 928-938. doi: 10.1109/TSP.2013.2297687.

SCHNITER P and RANGAN S. Compressive phase retrieval via generalized approximate message passing[J]. IEEE Transactions on Signal Processing, 2015, 63(4): 1043-1055. doi: 10.1109/Allerton.2012.6483302.

KINGSBURY N G. Complex wavelets for shift invariant analysis and filtering of signals[J]. Applied and Computational Harmonic Analysis, 2001, 10(3): 234-253. doi: 10.1006/acha. 2000.0343.

MEYER Y. Oscillating Patterns in Image Processing and Non-Linear Evolution Equations[M]. Boston: University Lecture Series, American Mathematical Society, 2001: 23-78.

BAUSCHKE H H, COMBETTES P L, and LUKE D R. Hybrid projection-reflection method for phase retrieval[J]. Journal of the Optical Society of America A, 2003, 20(6): 1025-1034. doi: 10.1364/JOSAA.20.001025.

CHI J N and ERAMIAN M. Enhancement of textural differences based on morphological component analysis[J]. IEEE Transactions on Image Processing, 2015, 24(9): 2671-2684. doi: 10.1109/TIP.2015.2427514.

ZHANG Zhengrong, ZHANG Jun, WEI Zhihui, et al. Cartoon-texture composite regularization based non-blind deblurring method for partly-textured blurred images with Poisson noise[J]. Signal Processing, 2015, 116(11): 127-140. doi: 10.1016/j.sigpro.2015.04.020.

GOLDSTEIN T and OSHER S. The split bregman method for L1-regularized problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(2): 323-343. doi: 10.1137/080725891.

DONOHO D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory, 1995, 41(3): 613-627. doi: 10.1109/18.382009.

BOYD S, PARIKH N, CHU E, et al. Distributed optimization and statistical learning via the alternating method of multipliers[J]. Foundations and Trends in Machine Learning, 2011, 3(1): 1-122. doi: 10.1561/2200000016.

WANG Yilun, YIN Wotao, and ZHANG Yin. A fast algorithm for image deblurring with total variation regularization[R]. CAAM Technical Report TR07-10, Rice University, Houston, 2007.

GLOWINSKI R. Lectures on Numerical Methods for Non-Linear Variational Problems[M]. Berlin: Bombay Springer-Verlag, 1980: 200-214.

WANG Z H, BOVIK A C, and SHEIKH H R. Image quality assessment: from error visibility to structural similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612.

RODRIGUEZ J A, XU Rui, CHEN Chienchun, et al. Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities[J]. Journal of Applied Crystallography, 2013, 46(2): 312-318. doi: 10.1107/ S0021889813002471.

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