基于核范数的JPEG解码算法  

A JPEG Decompression Algorithm Base on Nuclear Norm

作　　者：肖孝军 陈智斌[2] 甘小艇 XIAO Xiao-jun;CHEN Zhi-bin;GAN Xiao-ting(Guizhou College of Health Professions,554300,Tongren,Guizhou;Faculty of Science,Kunming University of Science and Technology,650500,Kunming;School of Mathematics and Statistics,Chuxiong Normal University,675000,Chuxiong,Yunnan,PRC)

机构地区：[1]贵州健康职业学院,贵州省铜仁市554300 [2]昆明理工大学理学院,昆明市650500 [3]楚雄师范学院数学与统计学院,云南省楚雄市675000

出　　处：《曲阜师范大学学报（自然科学版）》2018年第4期37-44,共8页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11761042)

摘　　要：针对低比特JPEG图像因量化过程中产生的量化噪声问题,提出一种核范数JPEG解码算法.首先基于自然图像的低秩性得到一个带无穷范数约束问题的低秩矩阵恢复模型,其次将约束凸优化问题转换为无约束优化问题,降低其计算难度.最后,利用经典的原对偶算法结合块匹配方法处理低秩矩阵模型,得到后处理JPEG解码图像.实验结果表明,该文算法比基于总变分后处理方法在去除量化噪声方面具有优越性.Focused on the quantization noise in low bit JPEG images which is generated because of rounding the in the quantization process, a nuclear norm based JPEG decompression algorithm is proposed. Firstly, the model of low rank matrix approximation with an infinite norm constraint is constructed based on low rank property of nature images; Secondly, constrained convex optimization problem is transformed into a unconstrained optimization problem to reduce its calculation difficulty; Finally, the classical primal dual algorithm and blocking match method are exploited to solve the low rank matrix model so that a post processing JPEG images can be obtained. The experimental results demonstrate that the proposed method has the superiority of removing the quantization noise than total variation methods.

关 键 词：JPEG算法 量化约束 核范数 块匹配方法 

分 类 号：TP391.73[自动化与计算机技术—计算机应用技术]