The iterative shrinkage method for impulsive noise reduction from images

In this paper, we present a novel scheme to compensate impulsive noise from images using the sparse shrinkage method. In this scheme, we assume the remaining noise after using a simple median filtering in place of corrupted pixels, found by boundary discriminative noise detection method, to be Gaussian additive noise. This assumption will later be verified by the means of simulation. Knowing that the pure image in the discrete wavelet transform (DWT) domain is a sparse vector, we define an optimization problem to minimize the l⁰-norm of the estimated image vector from the noisy one in the DWT domain. l⁰-norm makes the optimization problem a combinatorial optimization problem which is NP-hard to solve. To come up with a solution for our optimization problem, we convert the l⁰-norm problem to a continuous optimization problem which is then solved to find the estimated image with reduced noise. In the simulation and discussion part, the performance of our proposed method in reducing impulsive noise is compared to that of existing methods in the literature. We show that our proposed algorithm generally performs better in terms of both subjective and objective evaluations and is less complex.