Denoising images corrupted by impulsive noise using projections onto the epigraph set of the total variation function (PES-TV)

In this article, a novel algorithm for denoising images corrupted by impulsive noise is presented. Impulsive noise generates pixels whose gray level values are not consistent with the neighboring pixels. The proposed denoising algorithm is a two-step procedure. In the first step, image denoising is formulated as a convex optimization problem, whose constraints are defined as limitations on local variations between neighboring pixels. We use Projections onto the Epigraph Set of the TV function (PES-TV) to solve this problem. Unlike other approaches in the literature, the PES-TV method does not require any prior information about the noise variance. It is only capable of utilizing local relations among pixels and does not fully take advantage of correlations between spatially distant areas of an image with similar appearance. In the second step, a Wiener filtering approach is cascaded to the PES-TV-based method to take advantage of global correlations in an image. In this step, the image is first divided into blocks and those with similar content are jointly denoised using a 3D Wiener filter. The denoising performance of the proposed two-step method was compared against three state-of-the-art denoising methods under various impulsive noise models.