权重化QR分解的正交匹配追踪算法硬件实现  

Hardware Implementation of Orthogonal Matching Pursuit Algorithm for Weighted QR Decomposition

作　　者：王玺 梁文凯 杨虹[1] 张红升[1] 刘挺 牟晓霜 张磊 余柏汕 黎淼[1] WANG Xi;LIANG Wen-kai;YANG Hong;ZHANG Hong-sheng;LIU Ting;MOU Xiao-shuang;ZHANG Lei;YU Bai-shan;LI Miao(School of Optoelectronic Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学光电工程学院,重庆400065

出　　处：《电子学报》2024年第5期1534-1542,共9页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61604028);重庆市技术创新与应用发展专项重点项目(No.cstc2020jscx-gksbX0012);重庆市基础研究与前言探索重点项目(No.cstc2021ycjh-bgzxm0085)。

摘　　要：为在小型化、低成本的硬件平台实现正交匹配追踪(Orthogonal Matching Pursuit,OMP)算法,针对OMP算法中最小二乘法的问题,该文构造一个确定性的传感矩阵,提出一种低复杂度、低资源的权重化QR分解的OMP(Weighted QR decomposition OMP,WQR-OMP)算法硬件结构,在ZYNQ 7020型号芯片上搭建WQR-OMP SOC系统.WQR-OMP算法在传感矩阵进行QR分解后,根据三角矩阵R中元素的分布特性,通过权重化运算只保留主对角线上的元素而其他余元素归零,得到对角矩阵D,然后近似计算稀疏向量的解.实验结果表明:与基于QR分解的OMP(QR decomposition OMP,QR-OMP)和Batch-OMP算法的硬件结构相比,WQR-OMP算法硬件结构的重构速度更快、存储资源更少.在压缩率为0.25的条件下,WQR-OMP SOC系统对256×256分辨率图像的重构时间为400 ms左右,其速率比仅使用ARM处理器的重构速率提高了约6.3倍.与其他现有研究对比,该系统在Block RAM存储资源消耗较少的情况下,进一步提升了重构速度,适用于存储资源受限的硬件平台.To realize the orthogonal matching pursuit(OMP)algorithm on a miniaturized and low-cost hardware platform,for calculation of the least square method in the OMP algorithm,this paper constructs a deterministic perception matrix and proposes a low-complexity,low-resource weighted QR decomposition OMP(WQR-OMP)algorithm hardware architecture,and the WQR-OMP SOC system is built on the ZYNQ 7020 chip.The WQR-OMP algorithm is that after the QR decomposition of the sensing matrix according to the distribution characteristics of the elements in the triangular matrix R,the elements on the main diagonal are retained through the weighting operation,which returns other elements to zero to obtain the diagonal matrix D,and then approximately computes the solution for the sparse vector.The experimental results show that compared with the hardware architecture of OMP algorithm based on QR decomposition OMP(QR-OMP)and Batch-OMP algorithm,the WQR-OMP algorithm has lower computational complexity and fewer storage resources.The reconstruction time of the WQR-OMP SOC system is about 400 ms for 256×256 resolution images at a compression rate of 0.25,which is 6.3 times faster than the ARM processor does.Compared with other existing researchers,this system further improves the reconstruction speed with less consumption of Block RAM storage resources and is suitable for hardware platforms with limited storage resources.

关 键 词：正交匹配追踪算法 最小二乘 权重化 QR分解 ZYNQ 7020 

分 类 号：TN911.7[电子电信—通信与信息系统]