回溯正则化分段正交匹配追踪算法

针对分段正交匹配追踪（StOMP）算法对信号重构效果较差的问题，提出一种回溯正则化分段正交匹配追踪（BR-StOMP）算法。首先，该算法采用正则化思想选取能量较大的原子，以减少阈值阶段候选集中的原子；然后，利用回溯对原子进行检验，并对解的支撑集中的原子重新筛选一次，同时删除对解的贡献较低的原子，提高算法的重构率；最后，对感知矩阵进行归一化处理，使算法更加简单。仿真结果表明：BR-StOMP算法与正交匹配追踪（OMP）算法相比较峰值信噪比提高8%~10%左右，运行时间减少70%~80%；与StOMP算法相比较，峰值信噪比提高19%~35%。BR-StOMP算法能够精确地恢复信号，重建效果优于OMP算法和StOMP算法。

Backtracking regularized stage-wised orthogonal matching pursuit algorithm

The signal reconstitution result of Stage-wise Orthogonal Matching Pursuit (StOMP) algorithm is undesirable. In order to solve the problem, a new algorithm named Backtracking Regularized Stage-wise Orthogonal Matching Pursuit (BR-StOMP) was proposed. Firstly, atoms with larger energy were selected using the regularization method to reduce the number of atoms in candidate set of threshold stage. Then atoms were tested using backtracking, and the atoms in support set of solutions were filtered again. The atoms with little contribution to the result were deleted to increase the reconstitution ratio. Finally, the sensing matrix was normalized to make the algorithm more simple. The simulation results show that, compared with the Orthogonal Matching Pursuit (OMP) algorithm, the Peak Signal-to-Noise Ratio (PSNR) of the BR-StOMP algorithm is improved by 8% to 10% and its run time is reduced by 70% to 80%; compared with StOMP algorithm, the PSNR of the BR-StOMP algorithm is increased by 19% to 35%. The BR-StOMP algorithm can reconstruct the original signals accurately, and its reconstruction effect outperforms OMP algorithm and StOMP algorithm.