Sparse Code Shrinkage: Denoising by Nonlinear Maximum Likelihood Estimation

Such a representation is closely related to redundancy reductionand independent component analysis, and has some neurophysiological plausibility. In this paper, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a shrinkage nonlinearity on the components of sparse coding so as to reduce noise. Furthermore, we show how to choose the optimal sparse coding basis for denoising. Our method is closely related to the method of wavelet shrinkage, but has the important benefit over wavelet methods that both the features and the shrinkage parameters are estimated directly from the data. 1 Introduction A fundamental problem in neural network research is to find a suitable representation forthe data.