稀疏度自适应回溯追踪算法改进

针对压缩感知重构算法中信号稀疏度未知和步长大小固定的问题，提出一种新的压缩感知信号重构算法，即基于弱选择的稀疏度自适应回溯追踪（SPWAMP）算法。该算法将自适应思想、变步长迭代思想与回溯思想相结合，在未知信号稀疏度的情况下，利用阈值方法选取预选集，通过变步长更新支撑集原子个数并结合回溯思想剔除不可靠原子，最终实现信号精确重构。仿真结果表明，当信号稀疏度K达到65时，该算法重构精度相对稀疏度自适应匹配追踪（SAMP）算法提高了40%，而此时正交匹配追踪（OMP）算法、子空间追踪（SP）算法和分段弱选择正交匹配追踪（SWOMP）算法已无法实现重构。因此，该算法相对其它同类算法提高了信号重构精度。

Improved Algorithm for Sparsity Adaptive Backtracking

Aiming at the reconstruction of unknown sparsity signal and step size small fixed in compressed sensing， we put forward a new compression sensing signal reconstruction algorithm， namely sparsity adaptive backtracking algorithm based on weak selection（SPWAMP）. The algorithm combines the idea of adaptive， variable step iteration and backtracking. In the case of unknown signal sparsity，the preset is selected by threshold method， and the number of atoms in the support set is updated by variable step size and the idea of backtracking is used to eliminate the unreliable. Finally， the precise signal reconstruction is realized. Simulation results show that when the signal sparsity K reaches 65， the reconstruction accuracy of the algorithm is improved by 40% compared with SAMP， while OMP， SP and SWOMP cannot realize the reconstruction. Therefore， compared with other similar algorithms， this algorithm improves the signal reconstruction accuracy.