Multivariate statistical modeling for image denoising using wavelet transforms

TLDR: The general estimation rule in the wavelet domain is derived to obtain the denoised coefficients from the noisy image based on the multivariate statistical theory and a parametric multivariate generalized Gaussian distribution model is defined which closely fits the sample distribution.

Abstract: Recently a variety of efficient image denoising methods using wavelet transforms have been proposed by many researchers. In this paper, we derive the general estimation rule in the wavelet domain to obtain the denoised coefficients from the noisy image based on the multivariate statistical theory. The multivariate distributions of the original clean image can be estimated empirically from a sample image set. We define a parametric multivariate generalized Gaussian distribution (MGGD) model which closely fits the sample distribution. Multivariate model makes it possible to exploit the dependency between the estimated wavelet coefficients and their neighbours or other coefficients in different subbands. Also it can be shown that some of the existing methods based on statistical modeling are subsets of our multivariate approach. Our method could achieve high quality image denoising. Among the existing image denoising methods using the same type of wavelet (Daubechies 8) filter, our results produce the highest peak signal-to-noise ratio (PSNR).