基于压缩感知CoSaMP算法的精确重构

Accurate reconstruction of compressed sensing based on CoSaMP algorithm

为有效解决压缩采样匹配追踪(compressive sampling matching pursuit,Co Sa MP)算法对稀疏度K值的依赖问题,提高重构精度,提出了一种根据峰值信噪比增减变化趋势来确定最佳迭代次数的Co Sa MP改进算法。先将PSNR算式进行数学推导演变,将算式中未知的原始信号巧妙转换为已知信号,并证明了此转换式与PSNR算式有相同增减性,在迭代过程中基于此转换式可根据各列稀疏度的不同,自适应地确定不同列的最佳迭代次数,从而保证更高的重构精度。理论分析和实验仿真表明,改进的Co Sa MP算法比原有算法有更理想的重构效果,与其他重构算法相比有更高的重构成功率,并且更具高效性和实用性。

To solve the problem of the compressive sampling matching pursuit（CoSaMP） algorithm relies on the sparse K effectively, and to improve the reconstruction accuracy, this paper proposed an improved CoSaMP algorithm based on the peak signal to noise ratio change trend to determine the reasonable number of iterations. First, it studied the PSNR formula by mathematical derivation and evolution, the unknown original signal in the formula was skillfully converted to a known signal, moreover, it proved that this conversion formula and PSNR formula had the same fluctuation. In an iterative process based on this conversion formula, it could determined the optimal number of iterations of different columns adaptively according to the different sparsity of the columns, thus ensured greater accuracy of the reconstruction. Theoretical analysis and simulation results show that this improved CoSaMP algorithm not only has better results than the original algorithm in reconstruction, but also has a better reconstruction success rate and a more efficient and practical with other reconstruction algorithms.