Image denoising with parametric wavelet dictionary

In this paper we will introduce a new method on designing overcomplete dictionary from known wavelet function for the purpose of image denoising with sparse and redundant representation. Our work wants to show if a specific wavelet function is used for image denoising which set of these functions are optimized for image denoising using sparse approximation methods. In the context of sparse approximation, a suitable dictionary is a dictionary that is close to Equiangular Tight Frame (ETF) but for the purpose of image denoising with specific wavelet the variance and mean value of columns of Gram matrix of designed dictionary should be bounded; the bound value depends on desired functions. We formulate specific objective function with nonlinear constraint and then used Genetic Algorithm (GA) in order to find an optimum set of parameters for desired function in our goal. The algorithm is applied on Bspline wavelet function and the performance of our design has shown on image denoising.