The Properties of the Shear Gradient Operator and Its Application in Image Deblurring

The utilization of gradient operators is prevalent in image processing, as they effectively detect edges and provide directional information. However, these operators only differentiate the horizontal and vertical directions, ignoring details and causing loss of information in other directions. This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions. It investigates the properties of the shear gradient operator and proposes the shear total variation (STV) norm for image deblurring. By combining non-convex regularization to avoid excessive penalty and retain image details, a novel deblurring model integrating the STV norm and the L1/L2 minimization is proposed. The alternating direction method of multipliers (ADMM) algorithm is employed to solve this computationally challenging model, demonstrating exceptional performance in non-blind image deblurring through experiments.