SSIM-inspired image restoration using sparse representation

Abdul Rehman,Dominique Brunet,Edward R Vrscay,Zhou Wang,Mohammad Rostami

doi:10.1186/1687-6180-2012-16

Abdul Rehman, Dominique Brunet + Show 3 more

Open Access

https://doi.org/10.1186/1687-6180-2012-16

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Abstract

Recently, sparse representation based methods have proven to be successful towards solving image restoration problems. The objective of these methods is to use sparsity prior of the underlying signal in terms of some dictionary and achieve optimal performance in terms of mean-squared error, a metric that has been widely criticized in the literature due to its poor performance as a visual quality predictor. In this work, we make one of the first attempts to employ structural similarity (SSIM) index, a more accurate perceptual image measure, by incorporating it into the framework of sparse signal representation and approximation. Specifically, the proposed optimization problem solves for coefficients with minimum norm and maximum SSIM index value. Furthermore, a gradient descent algorithm is developed to achieve SSIM-optimal compromise in combining the input and sparse dictionary reconstructed images. We demonstrate the performance of the proposed method by using image denoising and super-resolution methods as examples. Our experimental results show that the proposed SSIM-based sparse representation algorithm achieves better SSIM performance and better visual quality than the corresponding least square-based method.

Highlights

In many signal processing problems, mean squared error (MSE) has been the preferred choice as the optimization criterion due to its ease of use and popularity, irrespective of the nature of signals involved in the problem
We proposed an algorithm to solve for the optimal coefficients for sparse and redundant dictionary in maximal structural similarity (SSIM) sense
We developed a gradient descent approach to achieve the best compromise between the distorted image and the image reconstructed using sparse representation

Summary

Introduction

In many signal processing problems, mean squared error (MSE) has been the preferred choice as the optimization criterion due to its ease of use and popularity, irrespective of the nature of signals involved in the problem. X where Y is the observed distorted image, X is the unknown output restored image, Rij is a matrix that extracts the (ij) block from the image, Ψ Î Rn x k is the dictionary with k >n, aij is the sparse vector of coefficients corresponding to the (ij) block of the image, Xis the estimated image, l is the regularization parameter, and W is the image obtained by averaging the blocks obtained using the sparse coefficients vectors αij calculated by solving optimization problem in (2) This is a local sparsity-based method that divides the whole image into blocks and represents each block sparsely using some trained dictionary Among other advantages, one major advantage of such a method is the ease to train a small dictionary as compared to one large global dictionary This is achieved with the help of (2) which is equivalent to (4). Solutions to the optimization problems in (5) and (6) are given in Sections 2.2 and 2.3, respectively

SSIM-optimal local model from sparse representation

NwB21B22

Conclusions

Repeat J times

Reconstruction Phase