用于压缩采样信号重建的回溯正则化自适应匹配追踪算法

正则化正交匹配追踪算法是一种广泛被使用的压缩感知重构算法，但其需要已知信号的稀疏度。针对这一缺点，本文提出一种回溯正则化自适应匹配追踪算法。该算法基于正则化正交匹配追踪算法进行改进，首先采用设置模糊阈值的方式初始化选取一些原子，然后对其进行正则化，最后采用回溯的方式删掉个别错误的原子。在每次迭代中，不断更新支撑集的同时扩大支撑集，以逐步逼近信号的稀疏度。实验结果表明，在相同的测试条件下，改进后的算法与其他贪婪算法相比，无论是对一维稀疏信号还是二维图像，均取得了更好的重建效果，且运行时间也比较适中。 

Backtracking Regularized Adaptive Matching Pursuit Algorithm for Signal Reconstruction of Compressive Sampling

Regularized orthogonal matching pursuit algorithm is a widely used reconstruction algorithm for compressive sampling, but it needs the sparsity of signal as a precondition. In order to overcome this disadvantage, a backtracking regularized adaptive matching pursuit algorithm is proposed, which aims at reconstructing the original signal when the sparsity is unknown. This algorithm is based on the regularized orthogonal matching pursuit algorithm. At beginning, fuzzy threshold is set for atoms selection, then the regularization processing is used to filter them. At last, some wrong atoms is deleted by using the backtracking method. The support set is updated while it is being enlarged gradually in every iteration, so it can approximate the sparsity of signal. Under the same condition, compared with the other greedy algorithms, the experimental results show that the superior reconstruction performance of the proposed algorithm for 1D sparse signal and 2D images and the running time is modest.