Abstract: To reconstruct the original signal from a set of linear measurements with noise, the cosparsity analytical model theory was analyzed and the hard thresholding orthogonal projection algorithm under the cosparsity analysis model was proposed. The cosparsity orthogonal projection strategy was used to improve the iterative process for the proposed algorithm, and the methods for selecting iterative step size and the length of cosparsity were given. The sufficient condition of convergence for the algorithm and the reconstructed signal error range between the reconstructed signal and the original one were provided. The experiments show that the CPU running time of the algorithm is only equal to 19%, 11% and 10% of AIHT, AL1 and GAP algorithms, and the average Peak Signal-to-Noise Ratio (PSNR) of reconstructed signal improves 0.89dB than that of AIHT but degrades a little bit than that of AL1 and GAP. It is concluded that the proposed algorithm can reconstruct the signal with Gaussion noise in high probability with very short running time or faster convergence speed than that of the current typical algorithm when some conditions are satisfied.

Key words: cosparsity analysis model, iteration, hard thresholding, orthogonal projection, signal reconstruction, compressed sensing

摘要： 为了从含噪声的测量矢量中重构信号，研究了稀疏补分析模型理论及其迭代硬阈值正交投影算法。通过采用稀疏补正交投影修改了稀疏补分析模型下迭代硬阈值算法的迭代追踪过程；分析了迭代步长和稀疏补取值大小对算法收敛速度和重构性能的影响，找出了选取最优迭代步长和最佳稀疏补取值方法；提出并实现了稀疏补分析模型下迭代硬阈值正交投影算法，给出了算法收敛的充分条件和重构信号误差范围。仿真实验结果表明，算法的平均运算时间仅仅为AIHT、AL1和GAP算法的19%、11%和10%；算法重构信号的综合平均峰值信噪比(PSNR)比AIHT算法提高了0.89dB，但比AIHT、AL1算法稍逊色。算法在满足给定条件下能够以高概率实现含噪信号重构，重构信号的综合平均PSNR与典型算相比没有明显下降，但运算时间大为缩短，收敛速度更快。

关键词: 稀疏补分析模型, 迭代, 硬阈值, 正交投影, 信号重构, 压缩感知