基于奇异值分解的可分离压缩成像方法  

Separable Compressive Imaging Method Based on Singular Value Decomposition

作　　者：张成[1,2] 汪东[1] 沈川[1] 程鸿[1] 陈岚[1] 韦穗[1] Zhang Cheng;Shen Chuan;Cheng Hong;Chen Lan;Wei Sui;Wang Dong(Key Laboratory of Intelligent Computing& Signal Processing (Anhui University),Ministry of Education,Hefei 230039;Key Laboratory of Modern Imaging and Displaying Technology of Anhui Province(Anhui University),Hefei 230039)

机构地区：[1]计算智能与信号处理教育部重点实验室(安徽大学),合肥230039 [2]安徽省现代成像与显示技术重点实验室(安徽大学),合肥230039

出　　处：《计算机研究与发展》2016年第12期2816-2823,共8页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(U1201255;61301296;61377006;61501001;61605002);安徽省自然科学基金项目(1608085QF161);安徽省高等学校自然科学研究项目(KJ2015A114;KJ2016A029)~~

摘　　要：可分离压缩传感可以通过一定比例的额外测量有效地解决压缩成像问题中面临的测量矩阵维数过大的瓶颈.但是现有可分离压缩传感(separable compressive sensing,SCS)方法需要2个可分离的测量矩阵都必须是行归一化后的正交随机矩阵,其显著地限制了该方法的应用范围.将奇异值分解(singular value decomposition,SVD)方法引入可分离可压缩传感测量过程,可以有效地实现测量矩阵和重建矩阵的分离:在感知阶段可以更多地考虑测量矩阵物理易于实现的性质,如Toeplitz或Circulant等确定性结构的矩阵;在重建阶段,更多地考虑测量矩阵的优化.通过引入奇异值分解对重建阶段的测量矩阵进行优化,可以有效地改善重建性能,尤其是Toeplitz或Circulant矩阵在大尺度图像的压缩重建情形.数值实验结果验证了该方法的有效性.When facing the compressive imaging problem that the measurement matrix has too largedimension,separable compressive sensing(SC S)can effectively achieve this problem at a cost of acertain percentage of additional measurements.However,the both separable measurement matrices inexisting separable compressive sensing method should be row-normalized orthogonal random matrix,which limits its application significantly.In this paper,the method of singular value decomposition(SVD)is introduced into separable compressive sensing measurement process,which can effectivelyachieve the separation of measurement matrix and reconstruction matrix:the design of themeasurement matrix in sensing stage is more to consider the physical properties for easyimplementations,such as the deterministic structure of Toeplitz or Circulant matrices and etc;in thereconstruction stage,it is more to consider the optimization of reconstruction matrix.Through theintroduction of singular value decomposition method to optimize the measurement matrix inreconstruction stage,the reconstruction performance can be effectively facilitated,especially forToeplitz and Circulant matrix in large-scale image compressive reconstruction.Numerical resultsdemonstrate the validity of our proposed method.

关 键 词：压缩成像 可分离压缩传感 可分离感知矩阵 奇异值分解 确定性矩阵 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TN911.7[自动化与计算机技术—计算机科学与技术]