An alternative minimization method for TV-image deblurring in tensor space

Abstract

The total variation (TV) model is a straightforward yet effective approach for noise reduction and blurring suppression in image processing. It necessitates converting the image matrix into a vector for problem-solving, which may compromise the preservation of the original image structure, especially in color images. In this paper, we propose a third-order tensor TV model for image deblurring in fractional-order differential form (t-FTV), based on the tensor t-product. We then develop a customized alternating minimization (AM) method to solve the tensor TV optimization problem. Next, we derive the optimality conditions for the t-FTV optimization problem and establish the convergence results of the proposed AM algorithm. Additionally, we compare the numerical performance of the proposed model against other methods for grayscale, color, and multispectral image deblurring. The results demonstrate that the proposed tensor TV model outperforms existing models.