Multiple Wavelet Basis Image Denoising Using Besov Ball Projections

Abstract

We propose a new image denoising algorithm that exploits an image's representation in multiple wavelet domains. Besov balls are convex sets of images whose Besov norms are bounded from above by their radii. Projecting an image onto a Besov ball of proper radius corresponds to a type of wavelet shrinkage for image denoising. By defining Besov balls in multiple wavelet domains and projecting onto their intersection using the projection onto convex sets (POCS) algorithm, we obtain an estimate that effectively combines estimates from multiple wavelet domains. While simple, the algorithm provides significant improvement over conventional wavelet shrinkage algorithms based on a single wavelet domain.