Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

A SVD based scheme for post processing of DCT coded images

In block discrete cosine transform (DCT) based image compression the blocking artifacts are the main cause of degradation, especially at higher compression ratio. In proposed scheme, monotone or edge blocks are identified by examining the DCT coefficients of the block itself. In the first algorithm of the proposed scheme, a signal adaptive filter is applied to sub-image constructed by the DC components of DCT coded image to exploit the residual inter-block correlation between adjacent blocks. To further reduce artificial discontinuities due to blocking artifacts, the blocky image is re-divided into blocks in such a way that the corner of the original blocks comes at the center of new blocks. These discontinuities cause the high frequency components in the new blocks. In this paper, these high frequency components due to blocking artifacts in monotone area are eliminated using singular value decomposition (SVD) based filtering algorithm. It is well known that random noise is hard to compress whereas it is easy to compress the ordered information. Thus, lossy compression of noisy signal provides the required filtering of the signal