Three-dimensional fractional total variation regularized tensor optimized model for image deblurring

Abstract

Image deblurring is an important pre-processing step in image analysis. The research for efficient image deblurring methods is still a great challenge. Most of the currently used methods are based on integer-order derivatives, but they typically lead to texture elimination and staircase effects. To overcome these drawbacks, some researchers have proposed fractional-order derivative-based models. However, the existing fractional-order derivative-based models only exploit nonlocal smoothness of spatial dimensions and fail to consider the other dimensional information for three-dimensional (3D) images. To address this issue, we propose a three-dimensional fractional total variation (3DFTV) based-model for 3D image deblurring problem. In this paper, we mathematically formulate the proposed model under the tensor algebra. Furthermore, we develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve our model. Experimental results demonstrate the superiority of our model against comparing models in terms of quality metrics and visual effects.