基于截尾估计的概率估计方法

能否以高概率正确重建稀疏信号是压缩感知理论中的重要研究内容。信号的稀疏度及冗余字典原子间的相关特性是研究该内容的关键因素。文中运用累积增量的概念，提出了一种基于截尾概率的累积增量满足约束界的概率估计的方法。运用该方法，判断能否利用选取的测量矩阵正确重构原始信号。通过Matlab仿真，验证了将高斯随机矩阵作为观测矩阵，在OMP重构算法下，可以高概率地正确重构出原始信号，也验证了文中所提方法的合理性。

Probability Estimation Method Based on Truncated Estimation

It＇s an important research content in compressive sensing theory whether reconstruct the sparse signals with a high probability. The sparsity of the signals and the relevant characteristics of the atoms in the redundant dictionary are the key factors of the study. In this paper, taking use of the concept of cumulative coherence, propose a probability estimation method to estimate the probability of the cumulative coherence which satisfies the constraint boundary that based on the truncated estimation. It can be found whether the selected measurement matrix can correctly reconstruct the original signal with this method. The Matlab simulation verifies that the original signal can be reconstructed using OMP algorithm with a high probability by taking the Gaussian random matrix as the measurement matrix, at the same time, it verifies that the proposed method is reasonable.