压缩感知理论是一种充分利用信号稀疏性或可压缩性的全新信号获取和处理理论.针对未知稀疏度信号重构,提出了一种改进的稀疏度自适应匹配追踪算法.该算法首先利用一种基于原子匹配测试的方法得到信号稀疏度的初始估计,然后在稀疏度自适应匹配追踪(SAMP)框架下采用变步长分阶段思想实现稀疏度的逼近,在初始阶段利用大步长实现稀疏度的快速粗接近,以提高收敛速度,在随后的迭代中逐渐减小步长,实现稀疏度的精逼近,最终实现信号的精确重构.理论分析和仿真结果表明,该算法在一定程度上解决了SAMP算法在大稀疏度条件下运算量较大以及固定步长导致的欠估计和过估计问题,较好地实现了未知稀疏度信号的精确重建,且重建性能和重建效率均优于现有的同类算法.%Compressive sensing is a novel signal sampling and processing theory under the condition that the signal is sparse or compressible. In this paper, a new Modified Sparsity Adaptive Matching Pursuit ( MSAMP) Algorithm is proposed for signal reconstruction without prior information of the sparsity. Firstly, a new sparsity estimation method based on atom matching test is used to get an initial estimation of sparsity. Then it realized the close approach of signal sparse step by step under the frame of sparsity Adaptive Matching Pursuit (SAMP). But the step size in MSAMP algorithm is variable rather than the fixed one in SAMP algorithm. At the beginning of step iterations, high value of step size, causing fast convergence of the algorithm is used initially to realise the coarse approach of signal sparse, and in the later step iterations smaller value of step size, advancing the performance of the algorithm is used to achieve the precise approach of signal sparse. Finally, it realized the precise reconstruction of sparse signal. The analytical theory and simulation results show that significant reconstruction performance improvement is achieved. The problem of over or under estimation in SAMP algorithm under the condition of large sparsity is almost resolved. Also, the convergence of the algorithm is much faster than the fixed step size algorithm.
展开▼
