Wavelet-based adaptive image deconvolution

This paper introduces an adaptive expectation-maximization (EM) algorithm for image restoration (deconvolution) formulated in the wavelet domain. The observed image is assumed to be a convolved and noisy version of the original image to be estimated. The restoration process is supported on prior knowledge about the original image, expressed in the wavelet coefficients, taking advantage of the sparsity of wavelet representations. Although similar formulations have been considered before, the resulting optimization problems have been computationally demanding and require offline tuning. The EM algorithm herein proposed combines the efficient image/signal representation offered by the discrete wavelet transform (OWT) with the diagonalization of the convolution operator provided by the discrete Fourier transform (OFT). The result is a very efficient iterative algorithm that requires D (N log N) operations per iteration. Moreover, by using a recently proposed parameter-free wavelet-domain prior, and by including the estimation of the noise variance in the EM steps, the resulting algorithm is fully data-adaptive.