稀疏补分析子空间追踪算法

Cosparsity analysis subspace pursuit algorithm

针对压缩感知理论的稀疏分析模型下的子空间追踪算法信号重构概率不高、重构性能不佳的缺点,研究了此模型下的稀疏补子空间追踪信号重构算法;通过选用随机紧支框架作为分析字典,设计了目标优化函数,改进优化了稀疏补取值方法,改进了算法迭代过程,实现了改进的稀疏补分析子空间追踪新算法(IASP)。实验结果证明,所提算法的信号完全重构概率明显高于分析子空间跟踪(ASP)等5种算法的信号完全重构概率;对于含高斯噪声的信号,所提算法重构信号的整体平均峰值信噪比明显超过ASP等3种算法整体平均峰值信噪比(PSNR),但略低于贪婪分析追踪(GAP)等2种算法的整体平均峰值信噪比。所提算法可用于语音和图像信号处理等领域。

As subspace pursuit algorithm under cosparsity analysis model in compressed sensing has the shortcomings of low completely successful reconstruction probability and poor reconstruction performance, a cosparsity analysis subspace pursuit algorithm was proposed. The proposed algorithm was realized by adopting the selected random compact frame as the analysis dictionary and redesigning target optimization function. The selecting method of cosparsity value and the iterated process were improved. The simulation experiments show that the proposed algorithm has obviously higher completely successful reconstruction probability than that of Analysis Subspace Pursuit（ ASP） and other five algorithms, and has higher comprehensive average Peak Signal-to-Noise Ratio（ PSNR） for the reconstructed signal than that of ASP and other three algorithms, but a little bit lower than that of Gradient Analysis Pursuit（ GAP） and other two algorithms when the original signal has Gaussion noise. The new algorithm can be used in audio and image signal processing.