Image deconvolution via efficient sparsifying transform learning

Image deconvolution is one of the most frequently encountered inverse problems in imaging. Since natural images can be modeled sparsely in some transform domain, sparsity priors have been shown to effectively regularize these problems and enable high-quality reconstructions. In this paper, we develop a data-adaptive sparse image reconstruction approach for image deconvolution based on transform learning. Our framework adaptively learns a patch-based sparsifying transform and simultaneously reconstructs the image from its noisy blurred measurement. This is achieved by solving the resulting optimization problem using an alternating minimization algorithm which has closed-form and efficient update steps. The performance of the developed algorithm is illustrated for an application in optical imaging by considering different optical blurs and noise levels. The results demonstrate that the developed method not only improves the reconstruction quality compared to the totalvariation based approach, but also is fast.