CLC number: TP391

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

剪切梯度算子的性质及其在图像去模糊中的应用

¹ School of Microelectronics and Data Science, Anhui University of Technology, Maanshan 243032, Anhui, China
² Origin Quantum Computing Company Limited, Hefei 234000, Anhui, China

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 November 2024

Abstract

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 $L_{\mathrm{1}}/L_{\mathrm{2}}$ 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.

摘要

在图像处理中，梯度算子的使用很普遍，因为它们能有效地检测边缘并提供方向信息。然而，这些算子仅区分水平和垂直方向，忽略了其他方向的细节，导致信息丢失。本文引入了剪切梯度算子来克服这一限制，能够在多个方向上精确捕捉细节，研究了剪切梯度算子的特性，并提出了用于图像去模糊的剪切全变分(STV)范数。通过结合非凸正则化以避免过度惩罚并保留图像细节，提出了一种结合 STV 范数和 L₁/L₂ 最小化的新型去模糊模型。采用交替方向乘子法(ADMM)算法来求解这个计算上具有挑战性的模型，实验表明其在非盲图像去模糊中表现出色。