I. Introduction
It has been widely recognized that image models reflecting the a priori knowledge—in the form of either regularization functional (in a deterministic setting) or prior probability distribution (in a statistical setting)—play a critical role in the performance of image recovery algorithms. Early heuristic observations about the local smoothness of image intensity field has been quantified by several mathematical tools in the literature, e.g., Lipschitz regularity [1, pp. 165–171] in harmonic analysis and total-variation (TV) [2] in variational calculus. Fast advances of wavelet theory in 1990s have shown the connection between smoothness characterization by Lipschitz regularity and nonlinear approximation by Besov-space functions [3]. The powerful class of wavelet thresholding techniques [4], [5] have found numerous recovery-related applications from deblocking [6] and inverse halftoning [7] to decomposition [8], [9] and inpainting. Similar nonlinear shrinkage techniques have also found effective for the class of discrete-cosine-transform (DCT) bases [10], [11] and geometric wavelets (e.g., curvelet denoising [12] and contourlet denoising [13]).