Compounded Regularization and Fast Algorithm for Compressive Sensing Deconvolution

Compressive Sensing Deconvolution (CS Deconvolution) is a new challenge problem encountered in a wide variety of image processing fields. A compound variational regularization model which combined total variation and curve let-based sparsity prior is proposed to recovery blurred image from compressive measurements. We propose a novel fast algorithm using variable-splitting and Dual Douglas-Rachford operator splitting methods. Experiments demonstrate our proposed algorithm can obtain high-resolution data from highly incomplete measurements.

[1]  M. Nielsen,et al.  Frame Decomposition of Decomposition Spaces , 2007 .

[2]  Trac D. Tran,et al.  Fast compressive sampling with structurally random matrices , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[3]  Andrés Almansa.  Sampling, interpolation and detection. Applications in satellite imaging. (Echantillonnage, interpolation et détection. Applications en imagerie satellitaire) , 2002 .

[4]  Michael Elad,et al.  Analysis versus synthesis in signal priors , 2006, 2006 14th European Signal Processing Conference.

[5]  Richard G. Baraniuk,et al.  ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems , 2004, IEEE Transactions on Signal Processing.

[6]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

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

[8]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[9]  E. Candès,et al.  New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .

[10]  Simon Setzer.  Splitting methods in image processing , 2009 .

[11]  Alfred S. Carasso,et al.  Singular Integrals, Image Smoothness, and the Recovery of Texture in Image Deblurring , 2003, SIAM J. Appl. Math..

[12]  D. Donoho.  Nonlinear Solution of Linear Inverse Problems by Wavelet–Vaguelette Decomposition , 1995 .

[13]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[14]  Jiaya Jia,et al.  High-quality motion deblurring from a single image , 2008, ACM Trans. Graph..

[15]  François-Xavier Le Dimet,et al.  Deblurring From Highly Incomplete Measurements for Remote Sensing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[16]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[17]  Simon Setzer,et al.  Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage , 2009, SSVM.

[18]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.