Spatially adaptive statistical modeling of wavelet image coefficients and its application to denoising

This paper deals with the application to denoising of a very simple but effective "local" spatially adaptive statistical model for the wavelet image representation that was recently introduced successfully in a compression context [1]. Motivated by the intimate connection between compression and denoising [2, 3, 4], this paper explores the significant role of the underlying statistical wavelet image model. The model used here, a simplified version of the one in [1], is that of a mixture process of independent component fields having a zero-mean Gaussian distribution with unknown variances sigma(2), that are slowly spatially-varying with the wavelet coefficient location s. We propose to use this model for image denoising by initially estimating the underlying variance field using a Maximum Likelihood (ML) rule and then applying the Minimum Mean Squared error (MMSE) estimation procedure. In the process of variance estimation, we assume that the variance field is "locally" smooth to allow its reliable estimation, and use an adaptive window-based estimation procedure to capture the effect of edges. Despite the simplicity of our method, our denoising results compare favorably with the best reported results in the recent denoising literature.