Simulated annealing based shift-variant image restoration using the multiresolution wavelet transform

We address the linear image restoration problem in the case of a spatially varying blur. Most of the time, the recovery of the original image from its degraded measurements is an ill-conditioned, underdetermined inverse problem. Here, stabilization is achieved via concave potential functions and minimization is carried out using Metropolis-type simulated annealing. Still, the ordinary approach can be subject to some convergence difficulties and it remains an ambitious challenge to take into account the mutual dependence between neighboring discontinuities. We first propose to improve convergence towards global minima through single-site updating in the discrete wavelet transform (DWT) space. For this purpose, a suitable restricted DWT space is introduced and it turns out that the resulting class of algorithms shows less sensitivity to the choice of the hyperparameters. Next, we show that the smoothness of the discontinuity field can be incorporated implicitly in a multiresolution framework by means of a simple penalty term defined on the high frequency channels