Image Deblurring Algorithm Using Block Augmented Lagrangian with Low Rank Gradients

Abstract

The proposed paper focuses on using Enhanced Augmented Lagrangian for image deblurring with some additional performance-enhancing parameters. In recent literature, high performance and several benefits have been demonstrated by restoring blurred images using Augmented Lagrangian methods. This paper proposes BLOCK AUGMENTED LAGRANGIAN WITH LOW RANK GRADIENTS (BALLORG) which is novel in the following ways: (i) faster convergence which leads to faster execution times. For most images the minimum is achieved with as little as 20 iterations, (ii) the use of derivatives and low rank together as regularization priors. The BALLORG begins with the lowest rank matrix, which is also the sparsest matrix available, and the final deblurred result is very successful in achieving good dB improvements through rank regulation; (iii) The penalty and regularization weights ensure that each iteration hits a global minimum with steep descent. The simulation experiments demonstrate how well the proposed BALLORG works when opposed to the other state-of-the-art approaches.