面向全变分图像复原的增广拉格朗日方法综述

Survey of Augmented Lagrangian Methods for Total Variation-based Image Restoration

图像复原旨在根据退化图像重建高品质原始图像,其复原的质量和速度问题一直都是图像处理领域研究的重要方向。由于其图像边缘保持特性,全变分(TV)最小化模型在图像复原领域取得了很大的成功。然而,全变分图像复原是一个典型的非光滑优化问题,需要发展相应的快速优化算法,而增广拉格朗日方法(ALM)则是近年来发展起来的一类代表性方法。结合相关进展,综述了全变分图像复原模型,变量分裂(VS)法和典型ALM算法,并通过实验从CPU运行时间、峰值信噪比(PSNR)和品质评价等方面分析了不同的变量分裂和ALM方法对图像复原性能的影响。

Image restoration aims to reconstruct the original image with high quality from the degraded image, where restoration quality and speed are always the major targets of image restoration. Total variation （TV） minimization model has achieved great success in image restoration due to its capability in preserving the edges of image. However, TV-based image restoration is a classic nonsmooth optimization problem, and thus fast optimization algorithms are required. One class of promising methods among the fast optimization algorithms is aug- mented Lagrangian method （ALM）. This paper provides a survey on TV-based image restoration model, variable splitting （VS）, and ALM algorithms. By conducting comparative experiments, the paper further discusses the influence of image restoration with different variable splitting and augmented Lagrangian methods based on the performance indicators of CPU time, peak signal to noise ratio （PSNR）, and im- age quality assessment.