On Denoising and Signal Representation

The problem of signal denoising using an orthogonal basis is considered. The framework of previous solutions converts the denoising 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 calculation of the coefficient estimation error in each subspace of the basis. For each subspace, we estimate such criterion and suggest to choose the subspace for which this quantity is minimized. An information theoretic interpretation of the proposed approach introduces a new minimum description length (MDL) method of denoising. By comparison of the MDL of families of bases we can find the basis which minimizes this criterion. This offers a new method of best basis search for representation of the noisy data.