摘要
考虑到投影矩阵对压缩感知(CS)算法性能的影响,该文提出一种优化投影矩阵的算法。该方法提出可导的阈值函数,通过收缩Gram矩阵非对角元的方法压缩投影矩阵和稀疏字典的相关系数,引入基于沃尔夫条件(Wolfe’s conditions)的梯度下降法求解最佳投影矩阵,达到提高投影矩阵优化算法稳定度和重构信号精度的目的。通过基追踪(BP)算法和正交匹配追踪(OMP)算法求解0l优化问题,用压缩感知方法实现随机稀疏向量、小波测试信号和图像信号的感知和重构。仿真实验表明,该文提出的投影矩阵优化算法能较大地提高重构信号的精度。
Considering the influence of the projection matrix on Compressed Censing （CS）, a novel method is proposed to optimize the projection matrix. In order to improve the signal＇s reconstruction precise and the stability of the optimization algorithm of the projection matrix, the proposed method adopts a differentiable threshold function to shrink the off-diagonal items of a Gram matrix corresponding to the mutual coherence between the projection matrix and sparse dictionary, and introduces a gradient descent approach based on the Wolf＇s-conditions to solve the optimization projection matrix. The Basis-Pursuit （BP） algorithm and the Orthogonal Matching Pursuit （OMP） algorithm are applied to find the solution of the minimum 10 -norm optimization issue and the compressed sensing are utilized to sense and reconstruct the random vectors, wavelet＇s noise test signals and pictures. The results of the simulation show the proposed method based on the projection matrix optimization is able to improve the quality of the reconstruction performance.
出处
《电子与信息学报》
EI
CSCD
北大核心
2015年第7期1681-1687,共7页
Journal of Electronics & Information Technology
基金
国家自然科学基金(61161010
11265001)
高等学校博士学科点专项科研基金(20133219110027)资助课题
关键词
压缩感知
相干性
基追踪算法
正交匹配追踪算法
Compressed Sensing （CS）
Mutual coherence
Basis-Pursuit （BP） algorithm
Orthogonal Matching- Pursuit （OMP） algorithm
