All Title Author
Keywords Abstract


Poissonian Image Deconvolution via Sparse and Redundant Representations and Framelet Regularization

DOI: 10.1155/2014/917040

Full-Text   Cite this paper   Add to My Lib

Abstract:

Poissonian image deconvolution is a key issue in various applications, such as astronomical imaging, medical imaging, and electronic microscope imaging. A large amount of literature on this subject is analysis-based methods. These methods assign various forward measurements of the image. Meanwhile, synthesis-based methods are another well-known class of methods. These methods seek a reconstruction of the image. In this paper, we propose an approach that combines analysis with synthesis methods. The method is proposed to address Poissonian image deconvolution problem by minimizing the energy functional, which is composed of a sparse representation prior over a learned dictionary, the data fidelity term, and framelet based analysis prior constraint as the regularization term. The minimization problem can be efficiently solved by the split Bregman technique. Experiments demonstrate that our approach achieves better results than many state-of-the-art methods, in terms of both restoration accuracy and visual perception. 1. Introduction Poissonian image deconvolution appears in various applications such as astronomical imaging [1], medical imaging [2], and electronic microscope imaging [3]. It aims to reconstruct a high quality image from the degraded image . Mathematically, the process of Poissonian image deconvolution can be generally modeled by where denotes the point spread function (PSF), denotes the unknown image to be estimated, denotes the Poisson noise process, denotes the blurred noisy image, and is the length of image vector which is stacked by columns. It is known that Poissonian image deconvolution is a typical ill-posed inverse problem. In general, the solution of (1) is not unique. Prior knowledge of image, including analysis-based and synthesis-based priors, can be used to address this problem. For an overview of the two classes of priors, we refer to [4]. Analysis-based priors are frequently used as regularization term in energy functional where is the regularization constraint term. Two main analysis-based methods have been proposed to solve problem (2): the total variation (TV) [5, 6] based methods and wavelet frames-based methods. TV-based methods have shown good performance on blurred images for discontinuous solution and edge-preserving advantages. Many authors have combined the TV regularization term with variant methods to solve problem (2). For example, Sawatzky et al. combined expectation-maximization algorithm with TV regularization [7] in positron emission tomography. Setzer et al. considered using TV regularization term with split

References

[1]  S.-M. Chao and D.-M. Tsai, “Astronomical image restoration using an improved anisotropic diffusion,” Pattern Recognition Letters, vol. 27, no. 5, pp. 335–344, 2006.
[2]  V. Y. Panin, G. L. Zeng, and G. T. Gullberg, “Total variation regulated EM algorithm,” IEEE Transactions on Nuclear Science, vol. 46, no. 6, pp. 2202–2210, 1999.
[3]  Y. Wang, Q. Dai, Q. Cai, P. Guo, and Z. Liu, “Blind deconvolution subject to sparse representation for fluorescence microscopy,” Optics Communications, vol. 286, pp. 60–68, 2013.
[4]  M. Elad, P. Milanfar, and R. Rubinstein, “Analysis versus synthesis in signal priors,” Inverse Problems, vol. 23, no. 3, pp. 947–968, 2007.
[5]  N. Dey, L. Blanc-Feraud, C. Zimmer et al., “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microscopy Research and Technique, vol. 69, no. 4, pp. 260–266, 2006.
[6]  L. Yan, H. Fang, and S. Zhong, “Blind image deconvolution with spatially adaptive total variation regularization,” Optics Letters, vol. 37, no. 14, pp. 2778–2780, 2012.
[7]  A. Sawatzky, C. Brune, F. Wiibbeling, T. Kosters, K. Sch?fers, and B. Martin, “Accurate EM-TV Algorithm in PET with Low SNR,” in Proceedings of the IEEE Nuclear Science Symposium Conference Record (NSS/MIC '08), pp. 5133–5137, October 2008.
[8]  S. Setzer, G. Steidl, and T. Teuber, “Deblurring Poissonian images by split Bregman techniques,” Journal of Visual Communication and Image Representation, vol. 21, no. 3, pp. 193–199, 2010.
[9]  J.-F. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,” Multiscale Modeling & Simulation, vol. 8, no. 2, pp. 337–369, 2009/10.
[10]  D.-Q. Chen and L.-Z. Cheng, “Deconvolving poissonian images by a novel hybrid variational model,” Journal of Visual Communication and Image Representation, vol. 22, no. 7, pp. 643–652, 2011.
[11]  M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Transactions on Image Processing, vol. 19, no. 12, pp. 3133–3145, 2010.
[12]  H. Fang, L. Yan, H. Liu, and Y. Chang, “Blind Poissonian images deconvolution with framelet regularization,” Optics Letters, vol. 38, no. 4, pp. 389–391, 2013.
[13]  H. Fang and L. Yan, “Poissonian image deconvolution with analysis sparsity priors,” Journal of Electronic Imaging, vol. 22, no. 2, pp. 023033-1–023033-10, 2013.
[14]  R. Rubinstein, T. Peleg, and M. Elad, “Analysis K-SVD: a dictionary-learning algorithm for the analysis sparse model,” IEEE Transactions on Signal Processing, vol. 61, no. 3, pp. 661–677, 2013.
[15]  Y. Xiao and T. Zeng, “Poisson noise removal via learned dictionary,” in Proceedings of the 17th IEEE International Conference on Image Processing (ICIP '10), pp. 1177–1180, September 2010.
[16]  M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Transactions on Image Processing, vol. 15, no. 12, pp. 3736–3745, 2006.
[17]  Y.-M. Huang, L. Moisan, M. K. Ng, and T. Zeng, “Multiplicative noise removal via a learned dictionary,” IEEE Transactions on Image Processing, vol. 21, no. 11, pp. 4534–4543, 2012.
[18]  M. M?kitalo and A. Foi, “Optimal inversion of the Anscombe transformation in low-count Poisson image denoising,” IEEE Transactions on Image Processing, vol. 20, no. 1, pp. 99–109, 2011.
[19]  M. Carlavan and L. Blanc-Féraud, “Sparse Poisson noisy image deblurring,” IEEE Transactions on Image Processing, vol. 21, no. 4, pp. 1834–1846, 2012.
[20]  W. Dong, L. Zhang, G. Shi, and X. Li, “Nonlocally centralized sparse representation for image restoration,” IEEE Transactions on Image Processing, vol. 22, no. 4, pp. 1620–1630, 2013.
[21]  L. Ma, L. Moisan, J. Yu, and T. Zeng, “A dictionary learning approach for Poisson image deblurring,” IEEE Transactions on Medical Imaging, vol. 32, no. 7, pp. 1277–1289, 2013.
[22]  J.-F. Cai, H. Ji, C. Liu, and Z. Shen, “Framelet-based blind motion deblurring from a single image,” IEEE Transactions on Image Processing, vol. 21, no. 2, pp. 562–572, 2012.
[23]  A. Ron and Z. Shen, “Affine systems in : the analysis of the analysis operator,” Journal of Functional Analysis, vol. 148, no. 2, pp. 408–447, 1997.
[24]  T. Goldstein and S. Osher, “The split Bregman method for -regularized problems,” SIAM Journal on Imaging Sciences, vol. 2, no. 2, pp. 323–343, 2009.
[25]  M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,” IEEE Transactions on Image Processing, vol. 19, no. 9, pp. 2345–2356, 2010.
[26]  Y. Huang, M. K. Ng, and Y.-W. Wen, “A fast total variation minimization method for image restoration,” Multiscale Modeling & Simulation, vol. 7, no. 2, pp. 774–795, 2008.
[27]  J. F. Cai, H. Ji, Z. Shen, and G. B. Ye, “Data-driven tight frame construction and image denoising. Applied and Computational Harmonic Analysis. In Press,” ftp://ftp.math.ucla.edu/pub/camreport/cam12-40.pdf.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal