The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable regularization term. Such problems with tensor format are of interest in many fields of applied mathematics such as image and video processing. Our goal in this paper is to address the solution of such problems with a more general form of the regularization term. An adapted iterative proximal gradient method is introduced for this purpose. Due to the slowness of the proposed algorithm, we use new tensor extrapolation methods to enhance its convergence. Numerical experiments on color image deblurring are conducted to illustrate the efficiency of our approach.

翻译：近端梯度法是一种用于处理优化问题中非光滑性的通用技术，其中目标函数表示为可微凸部分与不可微正则化项之和。此类具有张量形式的问题在图像与视频处理等应用数学领域备受关注。本文旨在解决具有更一般形式正则化项的此类问题，为此引入了一种自适应的迭代近端梯度法。鉴于所提算法收敛速度较慢，我们采用新型张量外推方法加速其收敛。通过彩色图像去模糊的数值实验验证了该方法的有效性。