A Kullback-Leibler divergence approach for wavelet-based blind image deconvolution

A new algorithm for wavelet-based blind image restoration is presented in this paper. It is obtained by defining an intermediate variable to characterize the original image. Both the original image and the additive noise are modeled by multivariate Gaussian process. The blurring process is specified by its point spread function, which is unknown. The original image and the blur are estimated by alternating minimization of the KullbackLeibler divergence between a model family of probability distributions defined using a linear image model and a desired family of probability distributions constrained to be concentrated on the observed data. The intermediate variable is used to introduce regularization in the algorithm. The algorithm presents the advantage to provide closed form expressions for the parameters to be updated and to converge only after few iterations. A simulation example that illustrates the effectiveness of the proposed algorithm is presented.