Adaptive total variation image deblurring: A majorization–minimization approach

This paper presents a new approach to image deconvolution (deblurring), under total variation (TV) regularization, which is adaptive in the sense that it does not 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 Bayesian prior interpretation of the TV regularizer. The resulting optimization problem is then attacked using a majorization–minimization algorithm. Although 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 showing that the proposed methodology achieves state-of-the-art performance, on par with TV-based methods with hand tuned regularization parameters, as well as with the best wavelet-based methods.