Image restoration in frequency domain using the EM algorithm

In this study, we extend the method presented in a recent paper (see Signal Process., vol.20, no.1, p.15, 1990), which considers the problem of the semicausal autoregressive (AR) parameter identification for images degraded by observation noise only. We propose a new approach to identify both the causal and semicausal AR parameters and blur parameters without a priori knowledge of the observation noise power and PSF of the degradation. We decompose the image into 1-D independent complex scalar subsystems resulting from the vector state-space model by using the unitary discrete Fourier transform (DFT). Then, by applying the expectation-maximization (EM) algorithm to each subsystem, we identify the AR model and blur parameters of the transformed image. The AR parameters of the original image are then determined by using the least squares (LS) method. The restored image is obtained as a by-product of the EM algorithm