Image denoising using wavelet thresholding and model selection

This paper describes wavelet thresholding for image denoising under the framework provided by statistical learning theory a.k.a. Vapnik-Chervonenkis (VC) theory. Under the framework of VC-theory, wavelet thresholding amounts to ordering of wavelet coefficients according to their relevance to accurate function estimation, followed by discarding insignificant coefficients. Existing wavelet thresholding methods specify an ordering based on the coefficient magnitude, and use threshold(s) derived under Gaussian noise assumption and asymptotic settings. In contrast, the proposed approach uses orderings better reflecting the statistical properties of natural images, and VC-based thresholding developed for finite sample settings under very general noise assumptions. A tree structure is proposed to order the wavelet coefficients based on its magnitude, scale and spatial location. The choice of a threshold is based on the general VC method for model complexity control. Empirical results show that the proposed method outperforms Donoho's (1992, 1995) level dependent thresholding techniques and the advantages become more significant under finite sample and non-Gaussian noise settings.