盲稀疏度下基于粒子滤波的稀疏信号重构

针对现有贪婪迭代类压缩感知重构算法对非高斯量测噪声抵抗性差的问题，提出一种盲稀疏度下基于粒子滤波的稀疏信号重构算法。该算法首先将鲁棒性更高的Huber损失函数替代常规的二次损失函数，用来增加对非高斯噪声的抵抗能力；并且引入粒子滤波实现对原始信号的最优估计，以削弱量测噪声的影响；最后在信号稀疏度未知的条件下，结合稀疏度自适应匹配追踪算法实现盲稀疏度下的原信号重构。理论分析和仿真结果表明，所提算法可以有效抵抗因非高斯噪声干扰或稀疏度未知导致的重构精度降低，且重构性能优于现有典型贪婪迭代类算法。

Particle Filtered Matching Pursuit for Compressive Sensing of Blind Sparsity Signal

In this paper, a particle filtered matching pursuit for compressive sensing of blind sparsity signal polluted by Non-Gaussion noise is proposed. While conventional detectors(e.g. least-squares estimates) are known to be sensitive to the Non-Gaussion nature of noise. The proposed algorithm which combines the Huber cost(loss) function with an l1-norm does not need the sparse prior while it eliminates the interference of measuring noise by particle filter estimation. Meanwhile, sparsity adaptive matching pursuit is used to sift the effective support set to inverse the original states. The results of simulation indicate that the proposed algorithm outperforms the existing greedy iterative inversions in the same condition, especially in the Non-Gaussion noise situation.