A new information-theoretic approach to signal denoising and best basis selection

The problem of signal denoising with an orthogonal basis is considered. The existing approaches convert the considered problem into one of finding a threshold for estimates of basis coefficients. In this paper, a new solution to the denoising problem is proposed. The method is based on the description length of the noiseless data in subspaces of the bases. For each subspace, we estimate the desired description length and suggest choosing the subspace for which this quantity is minimized. We provide a method of probabilistically estimating the reconstruction error. This estimate is used for probabilistic validation of the desired description length. In existing thresholding methods, the optimum threshold is obtained as a function of the additive noise variance. In practical problems, where the noise variance is unknown, the first step is to estimate the noise variance. The estimated noise variance is then used in calculating the optimum threshold. Unlike such approaches, in the proposed method, the noise variance estimation and the signal denoising are done simultaneously.