全变差正则化数据拟合问题产生于许多图像处理任务, 如图像去噪、去模糊、图像修复、磁共振成像、压缩图像感知等. 近年来, 求解此类问题的快速高效算法发展很快. 以最小二乘、最小一乘等为例简要回顾求解此类问题的主要算法, 并讨论一个全变差正则化非凸数据拟合模型在脉冲噪声图像去模糊问题中的应用.

Total variation regularized data fitting problems arise from a number of image processing tasks, such as denoising, deconvolution, inpainting, magnetic resonance imaging, and compressive image sensing, etc. Recently, fast and efficient algorithms for solving such problems have been developing very rapidly. In this paper, we focus on least squares and least absolute deviation data fitting and present a brief algorithmic overview for these problems. We also discuss the application of a total variation regularized nonconvex data fitting problem in image restoration with impulsive noise.