Integrating the EM algorithm with particle filter for image restoration with exponential dispersion noise

Images are often degraded during the data acquisition process. The degradation may involve blurring, information loss due to sampling, and various sources of noise. The purpose of image restoration is to estimate the original image from the degraded data. The present work sets forward a restoration technique for exponential dispersion noise based on Particle filtering (PF) using Hidden Markov Model. In order not to take observation information into account in general, the PF algorithm produced an incorrect sample from a discrete approximation distribution. To resolve this problem, we propose in the resampling stage of PF, samples which are generated from a continuous distribution rather than a discrete one based on Exponential Dispersion Models (EDM). An iterative approach, called the Expectation-Maximization (EM) algorithm, is used to find the maximum likelihood estimates of the relevant unknown parameters of the EDM. Moreover, under some conditions, the concavity of the conditional expected log-likelihood function is established in the maximization step of the EM algorithm. The proposed approach is rooted in ideas from statistics, control theory and signal processing. Experimental results are eventually displayed with simulation and satellite images, which demonstrate the good performance of the proposed approach.