Image restoration with 1/f-type fractal models and statistical estimation of the model parameters

A common problem in image processing is recovery of an image given noisy linear functionals of the original. While it has been shown that in certain situations, models possessing a 1/f-type power spectrum perform well as regularizers to stabilize these ill-posed inverse problems, the optimal parameters for the model are rarely known a priori. Previously, it was demonstrated that the expectation maximization (EM) algorithm can satisfactorily perform the estimation of the model parameters in the unblurred one-dimensional case. In this paper, we extend this analysis to the situation of two-dimensional objects and an environment which includes blurring. We show that again the EM algorithm performs well. In addition, we examine performance in terms of the variance of the estimates and bounds on these quantities.