Noise variance in signal denoising

Abstract

In the thresholding method of denoising the optimum threshold is obtained as a function of additive noise variance. In practical problems, where the variance of the noise is unknown, the first step is to estimate the noise variance. The estimated noise variance is then implemented in calculation of the optimum threshold. The current available methods of variance estimation are heuristic. Here, we provide a new method for estimation of the additive noise variance. The method is derived from a new denoising method which is proposed in Beheshti et al. (2002). Unlike thresholding approaches the denoising method in Beheshti is based on comparison of subspaces of the basis. It compares a defined description length (DL) of the noisy data in the subspaces. We show how the estimation of the noise variance and the denoising process can be done simultaneously.