The Statistical Modeling of Wavelet Coefficients as a Tool for Image De-noising

This paper proposes a spatially adaptive statistical model for wavelet image coefficients in order to perform image de-noising. The wavelet coefficients are modeled as zero-mean Gaussian random variables with high local correlation. This model is developed in a Bayesian framework, where a Maximum Likelihood (ML) estimator evaluates the variance of the blocks to which the wavelet subbands have been segmented. Then, applying the Minimum Mean Squared Error (MMSE) estimation procedure, the original or de-noised wavelet image coefficients are estimated. The reliable estimation of local variance is performed by making the assumption that variance is locally smooth. The validity of this assumption is boosted by segmenting the wavelet subbands into blocks of variable size. The segmentation employs quad-tree decomposition of the image and a linear transfer of the resulted tree on the wavelet subbands. This decomposition identifies object boundaries and defines more accurately the regions of smooth variance instead of dividing them in to blocks of fixed size. The extensive experimental evaluation, shows that the proposed scheme demonstrates very good performance as far as PSNR measures and visual quality are concerned with respect to others state of the art de-noising schemes.