低字典相干性K-SVD算法研究  

Research on Low Dictionary Coherence K-SVD Algorithm

作　　者：牛彪 李海洋[1] NIU Biao;LI Haiyang(School of Science,Xi'an Polytechnic University,Xi'an 710048)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《计算机与数字工程》2019年第1期92-98,共7页Computer & Digital Engineering

基　　金：国家自然科学基金(编号:11271297);陕西省自然科学基金(编号:2015JM1020)资助

摘　　要：K-SVD是非常经典的字典学习算法,该算法对稀疏系数矩阵和字典矩阵同时更新,在一定程度上提高了算法收敛速度,降低了运算复杂度。但是该算法得到的字典中噪音原子和无噪原子相似度高,因此字典的相干性较高。为了降低字典相干性,论文基于K-SVD算法,提出了一种低相干性字典学习的方法,即在K-SVD算法极小化目标函数下,添加了一项刻画字典相干性的惩罚项,并将学习得到的字典用于图像去噪。实验结果表明该方法不仅保证了信号恢复高度一致性和字典低相干性这两个目标,还提高了稀疏编码算法的收敛速度,从而在图像去噪中获得高质量的图像。K-SVD is a very classic dictionary learning algorithm.The algorithm updates the sparse coefficient matrix and the dictionary matrix at the same time,which improves the convergence speed of the algorithm and reduces the computational complexity.However,the noise atom and the noiseless atom in the learning dictionary are highly similar,so the coherence of the dictionary is relatively high.In order to reduce the dictionary coherence,this paper proposes a low coherence dictionary learning method based on the K-SVD algorithm and adds a penalty term for dictionary coherence under the K-SVD algorithm minimization objective function.The learned dictionary is used for image de-noising.The experimental results show that the proposed method not only guarantees the high consistency of signal recovery and low coherence of the dictionary,but also improves the convergence speed of the sparse coding algorithm,thus de-noising the image and high quality images are gotten.

关 键 词：K-SVD 字典学习 稀疏编码 相干性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]