半张量积压缩感知模型的快速重构方法  

Fast reconstruction method for compressed sensing model with semi-tensor product

作　　者：王金铭[1] 叶时平[1] 尉理哲[1] 许森[1] 蒋燕君[1] WANG Jinming;YE Shiping;YU Lizhe;XU Sen;JIANG Yanjun(Collage of Information Science&Technology,Zhejiang Shuren University,Hangzhou 310015,China)

机构地区：[1]浙江树人大学信息科技学院,浙江杭州310015

出　　处：《通信学报》2018年第7期26-38,共13页Journal on Communications

基　　金：浙江省自然科学基金资助项目(No.LY14E070001);浙江省公益技术应用研究计划基金资助项目(No.LGJ18F020001;No.LGG18F010007)~~

摘　　要：为降低随机观测矩阵在压缩感知应用中所需的存储空间,提升大尺寸图像重构的实时性,提出一种半张量积压缩感知方法。利用该方法构建低阶随机观测矩阵,对原始信号进行全局采样,随后将测量值进行分组处理并采用l_q-范数(0<q<1)迭代重加权方法进行重构。与传统压缩感知方法相比,所提方法既可成倍减小随机观测矩阵所需的存储空间,又可在保证图像重构质量的前提下,大大提升重构速度。验证实验利用了几种不同大小的随机观测矩阵对2维灰度图像进行了测试,比较其重构图像的峰值信噪比和重构时间。测试结果表明,利用所提方法在保证重构精度的前提下,可大大减小随机观测矩阵所需的存储空间(当降低为传统方法的1/4 096时,仍可得到与传统方法一致的重构质量),同时极大地提升重构的实时性,对于1 024像素×1 024像素大小的图像,其重构时间可提升近260倍。To reduce the storage space of random measurement matrix and improve the reconstruction efficiency for compressed sensing(CS),a new sampling approach for CS with semi-tensor product(STP-CS)was proposed.The proposed approach generated a low dimensional random measurement matrix to sample the sparse signals.Then the solutions of the sparse vector were estimated group by group with a lq-minimization(0<q<1)iteratively re-weighted least-squares(IRLS)algorithm.Compared with traditional compressed sensing methods,the proposed approach outperformed conventional CS in speed of reconstruction and that it also obtained comparable quality in the reconstruction.Numerical experiments were conducted using gray-scale images,the peak signal-to-noise ratio(PSNR)and the reconstruction time of the reconstruction images were compared with the random matrices with different dimensions.Comparisons were also conducted with other low storage techniques.Numerical experiment results show that the STP-CS can effectively reduce the storage space of the random measurement matrix to 1/4 096 and decrease tow orders of magnitude of time that for conventional CS,while maintaining the reconstruction quality.Numerical results also show that the reconstruction time can be effectively improved 260 for the image size of 1 024×1 024.

关 键 词：压缩感知 观测矩阵 半张量积 存储空间 重构时间 

分 类 号：TN911.73[电子电信—通信与信息系统]