Blurred Image Deconvolution Using Gaussian Scale Mixtures Model in Wavelet Domain

Image restoration (deconvolution) is a basic step for image processing, analysis and computer vision. We addressed blurred image deconvolution problem using Expectation maximization (EM) based approach in the wavelet domain. The sparsity property of wavelet coefficients is modelled using the class of Gaussian Scale Mixture (GSM), which represents the heavy-tailed statistical distribution. The maximum a posterior (MAP) estimate is computed using EM, where scale factors of GSM plays the role of hidden variables. The estimated hidden scaling variables are then used to restore the original image. Although similar formulations have been proposed before but the resulting optimization problems have been computationally demanding and sometimes depends heavily on the initial values of parameters. We proposed an optimized Bayesian approach in wavelet domain to restore an image degraded by linear distortion (e.g., blur) and additive Gaussian noise. Simulation results are presented to demonstrate the quality of our method, over a wide range of blur and noise level, both visually and in terms of signal to noise ratio.