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

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