Fast wavelet-based image deconvolution using the EM algorithm

This paper introduces an expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. The observed image is assumed to be a convolved and noisy version of the original image. The restoration process promotes a low-complexity reconstruction expressed in the wavelet coefficients, taking advantage of the well known sparsity of wavelet representations. Although similar formulations have been considered in previous work, the resulting optimization problems have been computationally demanding. The EM algorithm herein proposed combines the efficient image representation offered by the wavelet transform (DWT) with the diagonalization of the convolution operator provided by the FFT. The algorithm alternates between an FFT-based E-step and a DWT-based M-step, resulting in an efficient iterative process requiring O(NlogN) operations per iteration.