平滑零范数稀疏度约束下的盲稀疏回溯重构算法

现有的回溯迭代类算法具有重构速度快、精度高等优点，但实际中其需要已知信号稀疏度的条件有时难以满足。针对以上不足，提出了一种基于平滑零范数稀疏度约束的盲稀疏回溯重构算法，并证明了其收敛性。该算法不需已知稀疏度先验，在截断过程中以平滑零范数来估计信号的稀疏度并确定支撑集。新算法继承了现有回溯迭代类算法的有效性，同时避免了因稀疏度未知或估计不足导致的重构失败。理论分析和实验表明，新算法在无需信号稀疏度先验的条件下，重构性能优于现有典型回溯迭代类算法。

Blind Sparsity Back-Track Reconstruction Algorithm Based on Smooth L0 Norm Constraint

The existing back track iterative reconstruction algorithms for reconstructing the original signal fast and well always require the prior information of signal sparsity for accurate recovery. But sometimes it’s hard to meet the requirement in practice. Aiming at this problem, a new blind sparsity back track reconstruction algorithm based on smooth  0 norm constraint is proposed and its convergence is demonstrated. The new algorithm does not need the sparse prior and the smooth  0 norm issued to estimate the sparsity of signal and determine the support set in the truncation process. The new algorithm is effective as other back track ones and is able to avoid recovery failure due to unknown or underestimated sparsity as well. The theoretical analysis and experiment simulation prove that the performance of the new algorithm is better than that of the existing back track iterative reconstruction algorithms in the sparsity unknown conditions.