An Efficient Image Reconstruction Framework Using Total Variation Regularization with Lp-Quasinorm and Group Gradient Sparsity

Abstract

The total variation (TV) regularization-based methods are proven to be effective in removing random noise. However, these solutions usually have staircase effects. This paper proposes a new image reconstruction method based on TV regularization with Lp-quasinorm and group gradient sparsity. In this method, the regularization term of the group gradient sparsity can retrieve the neighborhood information of an image gradient, and the Lp-quasinorm constraint can characterize the sparsity of the image gradient. The method can effectively deblur images and remove impulse noise to well preserve image edge information and reduce the staircase effect. To improve the image recovery efficiency, a Fast Fourier Transform (FFT) is introduced to effectively avoid large matrix multiplication operations. Moreover, by introducing accelerated alternating direction method of multipliers (ADMM) in the method to allow for a fast restart of the optimization process, this method can run faster. In numerical experiments on standard test images sourced form Emory University and CVG-UGR (Computer Vision Group, University of Granada) image database, the advantage of the new method is verified by comparing it with existing advanced TV-based methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and operational time.