共轭梯度子空间基追踪算法及其相关结果

压缩感知可以在低于Nyqiust采样率条件下实现稀疏信号的精确恢复. 重构算法是压缩感知的主要研究内容之一. 本文基于子空间基追踪算法的回溯思想与共轭梯度法, 提出了共轭梯度子空间基追踪算法. 通过仿真实验验证了算法的有效性, 并讨论了该算法利用几种常见测量矩阵对稀疏信号的重构效果. 结果显示, 当测量矩阵为部分Fourier矩阵时, 该算法具有最优的重构效果.

Conjugate gradient subspace pursuit algorithm and related results

Compressed sensing can accurately recover sparse signals below Nyquist sampling rate. Reconstruction algorithm is one of the main research contents of compressed sensing. Based on the backtracking notion of subspace pursuit algorithm and conjugate gradient method, a conjugate gradient subspace pursuit algorithm is proposed in this paper. The effectiveness of the algorithm is verified through simulations, and the reconstruction effect of the algorithm on sparse signals is discussed using several common measurement matrices. The results show that the algorithm has the best reconstruction effect when the measurement matrix is a partial Fourier matrix.