Image De-noising based on the Statistical Modeling of Wavelet Coefficients and Quad-Tree Decomposition

This paper proposes a spatially adaptive statistical model for wavelet image coefficients in order to perform image de-noising. The wavelet coefficients are modelled 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 denoised 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 with two methods. The first method employs image quad-tree decomposition and transfers linearly 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 second method performs quad-tree decomposition of every subband with a variance splitting criterion. The subbands are segmented into blocks of nearly constant variance, so that the transform coefficients to be approximated as i.i.d random variables. 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. Index terms wavelets, de-noising, quad-tree decomposition.