基于分治试探的盲自适应匹配追踪重构算法

Blind adaptive matching pursuit algorithm for signal reconstruction based on sparsity trial and error

压缩感知是一种针对稀疏可压缩信号进行压缩采样的信号处理新方法,针对现有稀疏度探测方法中探测次数较多的问题,基于分治思想提出了盲稀疏度自适应匹配追踪(BSAMP)算法,首先分治试探信号稀疏度,使得其估计值快速逼近真实值,然后通过自适应分组并扩充信号支撑域的方法,快速筛选出有效支撑,并通过弱匹配剪枝得到重构信号。可以在信号稀疏度未知的情况下,快速估计出信号的稀疏度并精确重构出原信号。仿真实验表明,在相同条件下,该算法的重构时间比其他同类算法短,且重构概率也大于其他同类算法。

Compressed sensing is a novel signal processing theory that it introduces a novel way of acquiring compressible signals, the test times of existing sparsity trial and error algorithms were always large. The novel algorithm, blind sparsity adaptive matching pursuit （BSAMP） was proposed, could recover the original signal fast in the case of unknown sparsity. Firstly, the range of sparsity was determined, and each time half of values in current range were eliminated by trial and error test. Secondly, the number of atoms was twice the sparsity, which was united with the set of signal ap- proximation support （got by last iteration） and then reconstructed the signal by solving least-squares problems. Last but not least, the least-squares approximation was pruned by weakly matching for next iteration. The results of simulation show that the novel algorithm can reconstruct signal faster and get larger recovery probability than other similar algorithms in the same conditions.