Blind Deconvolution with Re-weighted Sparsity Promotion

Blind deconvolution has made significant progress in the past decade. Most successful algorithms are classified either as Variational or Maximum a-Posteriori (MAP ). In spite of the superior theoretical justification of variational techniques, carefully constructed MAP algorithms have proven equally effective in practice. In this paper, we show that all successful MAP and variational algorithms share a common framework, relying on the following key principles: sparsity promotion in the gradient domain, l2 regularization for kernel estimation, and the use of convex (often quadratic) cost functions. Our observations lead to a unified understanding of the principles required for successful blind deconvolution. We incorporate these principles into a novel algorithm that improves significantly upon the state of the art.

[1]  L. Rudin,et al.  Feature-oriented image enhancement using shock filters , 1990 .

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

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

[4]  Bryan C. Russell,et al.  Exploiting the sparse derivative prior for super-resolution , 2003 .

[5]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[6]  Anat Levin,et al.  User Assisted Separation of Reflections from a Single Image Using a Sparsity Prior , 2004, ECCV.

[7]  William T. Freeman,et al.  Removing camera shake from a single photograph , 2006, SIGGRAPH 2006.

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

[9]  Jiaya Jia,et al.  High-quality motion deblurring from a single image , 2008, SIGGRAPH 2008.

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

[11]  I. Daubechies,et al.  Iteratively reweighted least squares minimization for sparse recovery , 2008, 0807.0575.

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

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

[14]  Jian-Feng Cai,et al.  Blind motion deblurring from a single image using sparse approximation , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Sunghyun Cho,et al.  Fast motion deblurring , 2009, SIGGRAPH 2009.

[16]  Li Xu,et al.  Two-Phase Kernel Estimation for Robust Motion Deblurring , 2010, ECCV.

[17]  Jean Ponce,et al.  Non-uniform Deblurring for Shaken Images , 2012, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  Rob Fergus,et al.  Blind deconvolution using a normalized sparsity measure , 2011, CVPR 2011.

[19]  Bernhard Schölkopf,et al.  Fast removal of non-uniform camera shake , 2011, 2011 International Conference on Computer Vision.

[20]  Frédo Durand,et al.  Efficient marginal likelihood optimization in blind deconvolution , 2011, CVPR 2011.

[21]  Andrew Zisserman,et al.  Deblurring shaken and partially saturated images , 2011, ICCV Workshops.

[22]  Raanan Fattal,et al.  Blur-Kernel Estimation from Spectral Irregularities , 2012, ECCV.

[23]  Li Xu,et al.  Unnatural L0 Sparse Representation for Natural Image Deblurring , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[24]  Chao Wang,et al.  Nonedge-Specific Adaptive Scheme for Highly Robust Blind Motion Deblurring of Natural Imagess , 2013, IEEE Transactions on Image Processing.

[25]  Sylvain Paris,et al.  Handling Noise in Single Image Deblurring Using Directional Filters , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[26]  Justin K. Romberg,et al.  Blind Deconvolution Using Convex Programming , 2012, IEEE Transactions on Information Theory.

[27]  Haichao Zhang,et al.  Revisiting Bayesian blind deconvolution , 2013, J. Mach. Learn. Res..