An EM-based hybrid Fourier-wavelet image deconvolution algorithm

Blurred image restoration is a longstanding and critical research problem. We addressed this problem using Expectation Maximization (EM) based approach in wavelet domain. The sparsity property of wavelet coefficients is modeled using the class of Gaussian Scale Mixture (GSM), which represents the heavy-tailed statistical distribution, suitable for natural images. The underlying original image and noise parameters are estimated by alternating EM iterations based on available and hidden data sets, where regularization is introduced using an intermediate variable. Although similar formulations have been proposed before but the resulting optimization problems have been computationally demanding, where our formulation is simple to implement and converge in few iterations. Simulation results are presented to demonstrate the quality of our method both visually and in terms of signal to noise ratio improvement.