Image Denoising with Parametric Wavelet Dictionary
Keywords:
Equiangular Tight Frame, Genetic Algorithm,Bspline wavelet, Image Denoising.
Abstract:
In this paper we will introduce a new method ondesigning overcomplete dictionary from known wavelet function forthe purpose of image denoising with sparse and redundantrepresentation. Our work wants to show if a specific waveletfunction is used for image denoising which set of these functionsare optimized for image denoising using sparse approximationmethods. In the context of sparse approximation, a suitabledictionary is a dictionary that is close to Equiangular Tight Frame(ETF) but for the purpose of image denoising with specific waveletthe variance and mean value of columns of Gram matrix ofdesigned dictionary should be bounded; the bound value dependson desired functions. We formulate specific objective function withnonlinear constraint and then used Genetic Algorithm (GA) inorder to find an optimum set of parameters for desired function inour goal. The algorithm is applied on Bspline wavelet function andthe performance of our design has shown on image denoising.