基于压缩感知中观测矩阵优化和重构算法研究

发布时间：2018-06-20 20:31

本文选题：压缩感知 + 观测矩阵　；参考：《南京邮电大学》2017年硕士论文

【摘要】：压缩感知是一种新兴起的采样理论,信号在采样的同时完成了压缩,打破了的传统Nyquist采样定理。压缩感知充分依据信号是可稀疏的,利用非自适应线性投影来尽量保留原始信号的信息,并利用数值凸优化精确解析重构信号。本文主要针对压缩感知中观测矩阵优化与重构算法设计这两部分做了以下研究:1.介绍了梯度下降法与QR分解原理,提出一种新的观测矩阵优化。并对它进行实验仿真,与现有的几种矩阵优化方法对比分析,此优化方法在提高峰值信噪比和重构稳定性方面具有较好的效果。2.具体介绍了增大矩阵列独立性的矩阵分解原理,并利用梯度下降法降低观测矩阵同稀疏矩阵之间的相关性,将二者相结合进一步改进观测矩阵。对比仿真实验结果表明,新矩阵具有较好的重构性能。3.提出了一种将改进的观测矩阵与共轭梯度法相结合的算法。针对于共轭梯度重构算法,优化其观测矩阵,得到新的重构算法,此算法保留了观测矩阵优化OMP算法的稳定性和鲁棒性,同时又具备共轭梯度算法的严谨性。实验仿真表明,改进后观测矩阵的共轭梯度算法的重构时间大大减少,并证实了其可行性与优越性。
[Abstract]:Compression sensing is a new sampling theory. The signal is compressed at the same time, which breaks the traditional Nyquist sampling theorem. Compression sensing is based on the sparsity of the signal, the non-adaptive linear projection is used to keep the original signal information as much as possible, and the numerical convexity optimization is used to accurately analyze the reconstructed signal. In this paper, we focus on the optimization and reconstruction algorithm design of observation matrix in compressed sensing, and do the following research: 1. The gradient descent method and QR decomposition principle are introduced, and a new optimization of observation matrix is proposed. The simulation results are compared with the existing matrix optimization methods. The results show that this optimization method can improve the PSNR and the reconstruction stability. 2. The principle of matrix decomposition to increase the independence of matrix column is introduced in detail, and the correlation between observation matrix and sparse matrix is reduced by gradient descent method, and the observation matrix is further improved by combining the two methods. The simulation results show that the new matrix has good reconstruction performance. 3. An algorithm combining the improved observation matrix with the conjugate gradient method is proposed. For the conjugate gradient reconstruction algorithm, the observation matrix is optimized, and a new reconstruction algorithm is obtained. This algorithm preserves the stability and robustness of the observation matrix optimization OMP algorithm and has the preciseness of the conjugate gradient algorithm at the same time. The experimental results show that the reconstruction time of the conjugate gradient algorithm of the improved observation matrix is greatly reduced and the feasibility and superiority of the algorithm are verified.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

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