计算机应用研究2017，Vol.34Issue(7)：1950-1952,3.DOI:10.3969/j.issn.1001-3695.2017.07.006
自适应梯度下降观测矩阵优化算法
Adaptive gradient descent optimization algorithm for measurement matrix
摘要
Abstract
Based on the mutual correlation between measurement matrix and sparse matrix in compressed sensing(CS),it can improve the quality of reconstructed signal by reducing the correlation coefficient.Combining with the gradient descent idea of unconstrained convex optimization problem,this paper proposed an adaptive gradient descent(AGD) algorithm.First,it shrinked the Gram matrix of sensing matrix using equiangular tight frame(ETF) theory.Then,it established an unconstrained convex optimization problem over Gram matrix.Finally,it could obtain the optimized measurement matrix by the adaptive gradient descent method.By updating the direction of gradient descent during each iteration,it could make the Gram matrix approximate ETF in the shortest time.Simulation results show that this algorithm not only requires fewer iterations,but reduces the mutual correlation greatly between measurement matrix and sparse matrix.The proposed method demonstrates better performance than conventional optimization methods.关键词
压缩感知/观测矩阵/自适应梯度下降/互相关性/等角紧框架Key words
compressed sensing(CS)/measurement matrix/adaptive gradient descent(AGD)/mutual correlation/equiangular tight frame(ETF)分类
信息技术与安全科学引用本文复制引用
蒋伊琳,佟岐,张荣兵,王海艳,汲清波..自适应梯度下降观测矩阵优化算法[J].计算机应用研究,2017,34(7):1950-1952,3.基金项目
国家自然科学基金资助项目(61571146) （61571146）
黑龙江省自然科学基金资助项目(F201407) （F201407）
中央高校基本科研业务费专项资金资助项目(HEUCF160803) （HEUCF160803）
