Abstract: In this paper, a novel statistical model is proposed to describe the Gaussian noisy compressed sensing problem with Gaussian random measurement matrix, and under the statistical framework, some hypothesis tests are used to analyse the performance of the weighted median regression estimate compressive sensing signal reconstruction with an iterative hard threshold under the [l0-]regularized constraint. The[χ2]test based computation sequence is proposed to improve the performance of its coordination descent computation sequence, and F test based data adaptive stopping criterion is presented to take the place of its manual stopping conditions of the maximal number of iterations and the lower bound of the residual energy. Practical performance of the proposal is evaluated via numerical experiments.

Key words: compressing sensing, Gaussian noise, [l0-]regularized least absolute deviation, weighted median, hypothesis testing

摘要： 对高斯噪声下的高斯随机观测矩阵压缩感知问题建立了新的统计模型，并在该统计模型的基础上，引入相应的统计检验方法对[l0]范式约束下的硬阈值加权中值回归重建算法进行分析。提出了基于卡方检验的[l1]范式支持检测计算顺序排序方法来改进该算法的坐标下降的计算顺序；针对该算法需要通过人工设定最大迭代次数和残差能量下界来控制迭代次数的问题，提出了基于F检验的自适应停止准则，并在仿真实验中证明了改进后算法的有效性。

关键词: 压缩感知, 高斯噪声, [l0]范式最小绝对偏差, 加权中值, 假设检验