Adaptive total variation image deblurring: A majorization-minimization approach

This paper presents a new approach to total variation (TV) based image deconvolution/deblurring, which is adaptive in the sense that it doesn’t require the user to specify the value of the regularization parameter. We follow the Bayesian approach of integrating out this parameter, which is achieved by using an approximation of the partition function of the probabilistic prior interpretation of the TV regularizer. The resulting optimization problem is then attacked using a majorization-minimization algorithm. Although the the resulting algorithm is of the iteratively reweighted least squares (IRLS) type, thus suffering of the infamous “singularity issue”, we show that this issue is in fact not problematic, as long as adequate initialization is used. Finally, we report experimental results which show that the proposed methodology achieves state-of-the-art performance, on par with TVbased methods with hand tuned regularization parameter, as well as with the top wavelet-based methods.