Fast total variation deconvolution for blurred image contaminated by Poisson noise

The algorithm focuses on restoring blurred image contaminated by Poisson image.The algorithm uses the variable splitting technique to simply the problem.The algorithm runs very fast and the restored image is of high quality.The algorithm is easy to be extended to solve other optimization problem. In this paper, we present a fast non-blind deconvolution method for restoring blurred images contaminated by Poisson noise. The problem is formulated by finding the minimizer of the negative logarithmic Poisson log-likelihood combined with the total variation (TV). To attack the challenging task, we adopt the well-known variable splitting and penalty technique to convert the problem into two easier sub-problems: one is a modified TV regularized deconvolution and the other is a simple convex optimization problem. Experimental results show that the proposed method runs very fast and the quality of the restored image is comparable with that of some state of the art methods.

[1]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[2]  M. Bertero,et al.  Image deblurring with Poisson data: from cells to galaxies , 2009 .

[3]  P. Green.  Bayesian reconstructions from emission tomography data using a modified EM algorithm. , 1990, IEEE transactions on medical imaging.

[4]  Jeffrey A. Fessler,et al.  Parallel MR Image Reconstruction Using Augmented Lagrangian Methods , 2011, IEEE Transactions on Medical Imaging.

[5]  Frédo Durand,et al.  Understanding and evaluating blind deconvolution algorithms , 2009, CVPR.

[6]  José M. Bioucas-Dias,et al.  Restoration of Poissonian Images Using Alternating Direction Optimization , 2010, IEEE Transactions on Image Processing.

[7]  Giuseppe Vicidomini,et al.  Automatic deconvolution of 4Pi-microscopy data with arbitrary phase. , 2009, Optics letters.

[8]  Yang Song,et al.  Split Bregmanized anisotropic total variation model for image deblurring , 2015, J. Vis. Commun. Image Represent..

[9]  Michael K. Ng,et al.  A Fast Total Variation Minimization Method for Image Restoration , 2008, Multiscale Model. Simul..

[10]  Fang Li,et al.  An efficient nonconvex regularization for wavelet frame and total variation based image restoration , 2015, J. Comput. Appl. Math..

[11]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[12]  A. Tikhonov.  On the stability of inverse problems , 1943 .

[13]  Mário A. T. Figueiredo,et al.  Deconvolution of Poissonian images using variable splitting and augmented Lagrangian optimization , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[14]  Yongdong Zhang,et al.  A Highly Parallel Framework for HEVC Coding Unit Partitioning Tree Decision on Many-core Processors , 2014, IEEE Signal Processing Letters.

[15]  Giuseppe Vicidomini,et al.  Automatic deconvolution in 4Pi-microscopy with variable phase. , 2010, Optics express.

[16]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[17]  Rob Fergus,et al.  Fast Image Deconvolution using Hyper-Laplacian Priors , 2009, NIPS.

[18]  Houzhang Fang,et al.  Blind image deconvolution with spatially adaptive total variation regularization. , 2012, Optics letters.

[19]  Françoise Viallefont-Robinet,et al.  Improvement of the edge method for on-orbit MTF measurement. , 2010, Optics express.

[20]  Gabriele Steidl,et al.  Deblurring Poissonian images by split Bregman techniques , 2010, J. Vis. Commun. Image Represent..

[21]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[22]  Yongdong Zhang,et al.  Parallel deblocking filter for HEVC on many-core processor , 2014 .

[23]  Tony F. Chan,et al.  Total variation blind deconvolution , 1998, IEEE Trans. Image Process..

[24]  Li Qi,et al.  An improved Richardson–Lucy algorithm based on local prior , 2010 .

[25]  Qi Li,et al.  High quality non-blind image deconvolution using the Fields of Experts prior , 2013 .

[26]  L. Lucy.  An iterative technique for the rectification of observed distributions , 1974 .

[27]  Dai-Qiang Chen,et al.  Regularized Generalized Inverse Accelerating Linearized Alternating Minimization Algorithm for Frame-Based Poissonian Image Deblurring , 2014, SIAM J. Imaging Sci..

[28]  D. A. Fish,et al.  Blind deconvolution by means of the Richardson-Lucy algorithm. , 1995 .

[29]  Josiane Zerubia,et al.  Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution , 2006, Microscopy research and technique.

[30]  José M. Bioucas-Dias,et al.  Total Variation-Based Image Deconvolution: a Majorization-Minimization Approach , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[31]  Weiguo Gong,et al.  Total variation blind deconvolution employing split Bregman iteration , 2012, J. Vis. Commun. Image Represent..

[32]  Houzhang Fang,et al.  Poissonian Image Deconvolution via Sparse and Redundant Representations and Framelet Regularization , 2014 .

[33]  J. Bardsley,et al.  Tikhonov regularized Poisson likelihood estimation: theoretical justification and a computational method , 2008 .

[34]  M. Burger,et al.  Accurate EM-TV algorithm in PET with low SNR , 2008, 2008 IEEE Nuclear Science Symposium Conference Record.

[35]  Frédo Durand,et al.  Image and depth from a conventional camera with a coded aperture , 2007, SIGGRAPH 2007.

[36]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[37]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .

[38]  Qi Li,et al.  Non-blind image deconvolution using natural image gradient prior , 2013 .

[39]  Yongdong Zhang,et al.  Efficient Parallel Framework for HEVC Motion Estimation on Many-Core Processors , 2014, IEEE Transactions on Circuits and Systems for Video Technology.

[40]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

[41]  Jeffrey A. Fessler,et al.  A Splitting-Based Iterative Algorithm for Accelerated Statistical X-Ray CT Reconstruction , 2012, IEEE Transactions on Medical Imaging.

[42]  Edmund Y Lam,et al.  Maximum a posteriori blind image deconvolution with Huber-Markov random-field regularization. , 2009, Optics letters.

[43]  Mario Bertero,et al.  Introduction to Inverse Problems in Imaging , 1998 .

[44]  Laure Blanc-Féraud,et al.  Sparse Poisson Noisy Image Deblurring , 2012, IEEE Transactions on Image Processing.

[45]  Françoise Viallefont-Robinet.  Edge method for on-orbit defocus assessment. , 2010, Optics express.

[46]  Qi Li,et al.  A piecewise local regularized Richardson–Lucy algorithm for remote sensing image deconvolution , 2011 .