基于压缩感知和改进自适应正交匹配的稀疏信号重构

Sparse Signal Reconstruction Based on Compressed Sensing and Adaptive Orthogonal Matching

针对传统香农-奈奎斯特采样定理指出在保证原始信号重构精度的前提下,采样频率必须为原始信号频率的2倍,提出了一种基于压缩感知理论和改进的自适应正交匹配追踪算法的稀疏信号重构方法;首先引入了压缩感知模型和信号重构目标函数,然后在对经典正交匹配追踪类算法进行分析和总结的基础上,为克服其不足,设计了一种二次筛选支配原子集的方法,即通过计算信号的QR分解并计算具有最大势能的原子从而得到能量候选原子集,通过计算余量与原子的相关性选出相关性最大的原子从而得到相关候选原子集,并将能量候选原子集和相关候选原子集的交集作为最终支配原子集;最后定义了具体的采用自适应正交匹配算法实现信号重构的算法;在Matlab仿真环境下试验,结果表明:文章方法能有效地进行稀疏信号重构,具有较小的重构误差,且与其它方法相比,具有收敛速度快和重构效果好的优点。

Aiming at the traditional Shannon--Nyquist sample theorem argued that under the guarantee of signal reconstruction accura- cy, the sampling frequency should be two times more than the primitive signal sampling frequency, a sparse signal construction method based on compressed sensing and improved adaptive orthogonal matching was proposed. Firstly, the compressed sensing and signal construction function was set, then the classic orthogonal matching pursuit algorithm was summarized, and the atom re--selection method was designed, namely, by computing the QR decomposition of signal and energy selective set, and by computing the relation between remain value and atom to get the relative selective atom set, and the intersection between energy selective atom set and relative selective set was built as the final supporting atom set. Finally, the algorithm for signal construction was defined. The simulation experiment was operated in Matlab environ- ment, and the result shows the method can realize sparse signal construction with less construction error, and compared with the other meth- ods, it has the advantage of rapid convergence and good construction effect.