变分正则化图像复原模型与算法综述  

An Overview of Image Restoration Based on Variational Regularization

作　　者：樊启斌[1] 焦雨领[1] 

机构地区：[1]武汉大学数学与统计学院,武汉湖北430072

出　　处：《数学进展》2012年第5期531-546,共16页Advances in Mathematics（China）

基　　金：国家自然科学基金项目(No.61179039);国家重点基础研究发展计划(973)项目(No.2011CB707100);国家自然科学基金重点项目(No.40930532)

摘　　要：图像复原就是对图像退化模型进行处理以恢复图像的原始信息.由于引起图像退化的因素和性质各不相同,所以图像复原是一个复杂的数学过程,本质上是求解不适定的反问题.本文综述了变分正则化图像复原模型与算法.首先,系统阐述了图像复原中的去噪(分解)模型、去模糊模型、修复模型.其次,构建了一个统一的变分正则化图像复原模型并总结了各种典型的数值求解方法.最后,指出在今后进一步研究中值得关注的8个问题.Image restoration is a complicated process in which the original information can be recovered from the degraded image model caused by lots of factors. Mathematically, image restoration problems are ill-posed inverse problems. In this paper image restoration models and algorithms based on variational regularization are surveyed. First, we review and analyze the typical models for denoising, deblurring and inpainting. Second, we construct a unified restoration model based on variational regularization and summarize the typical numerical methods for the model. At last, we point out eight difficult problems which remain open in this field.

关 键 词：正则化 图像复原 反问题 全变差 小波 

分 类 号：TP317.4[自动化与计算机技术—计算机软件与理论]