压缩感知中迭代重构算法研究及应用

发布时间：2018-04-25 09:25

本文选题：压缩感知 + 重构算法　；参考：《湘潭大学》2017年硕士论文

【摘要】：随着科技的进步,大量的传感器被投入使用,而这些设备采用奈奎斯特定理采样虽然对信号可实现精确重构,但是带来海量的数据采集、传输和存储,且奈奎斯特采样定理依赖信号的带宽。压缩感知的提出突破奈奎斯特采样定理的限制,不依赖信号的带宽,而是基于信号的稀疏性。压缩感知重构算法是压缩感知中尤为重要的部分,本文致力于优化压缩感知重构算法,提升算法的重构性能,提出一种平滑L0范数最小化的迭代重构算法和一种分布式压缩感知中自适应阈值迭代重构算法。本文的主要研究工作如下:提出一种平滑L0范数的迭代重构算法。一种平滑L0范数的迭代重构算法是一种复杂度较低,高准确率的重构方法。首先,在平滑L0范数上,本文采样两种函数逼近L0范数,求解平滑L0范数问题,采用梯度下降方法,得到迭代公式,在每一步迭代中,计算迭代公式,得到迭代结果,获取其对应的支撑集,采用支撑集对迭代结果进行修正,使得残差更小。当达到迭代停止条件,则停止迭代过程。相比于对比算法,该方法可达到更高的重构精度,同时其复杂度相对较低,对二维Lena图像进行重构时,在不同的采样率的情况下,本文提出的方法在采样率较低的情况下,重构信号的PSNR明显高于其他的对比算法,存在着明显的优势。提出一种分布式压缩感知中自适应阈值迭代重构算法,针对网络模型中,在分布式的场景下,采用分布式压缩感知的信号模型建模,该方法是一种分散式并行算法。假设网络中的节点本身具有一定的计算能力,每个节点将自身重构的支撑集发送给周围节点,节点收到周围节点的支撑集,对支撑集进行融合操作,最终反馈给周围的节点,多次信息交互后,即可得到正确的支撑集。该方法不仅有效减少网络中数据量的传递,采用并行的算法,重构速度更快。实验表明,该算法应用于有信号噪声的无线网络中,能完美重构出原始信号。
[Abstract]:With the development of science and technology, a large number of sensors have been put into use, and these devices use Nyquist theorem sampling, although the signal can be accurately reconstructed, but it brings massive data acquisition, transmission and storage. The Nyquist sampling theorem depends on the bandwidth of the signal. Compression sensing is proposed to break through the Nyquist sampling theorem, which does not depend on the bandwidth of the signal, but based on the sparsity of the signal. Compression sensing reconstruction algorithm is an important part of compression perception. This paper is devoted to optimizing the compression perception reconstruction algorithm to improve the performance of the algorithm. An iterative reconstruction algorithm with smooth L0 norm minimization and an adaptive threshold iterative reconstruction algorithm in distributed compression perception are proposed. The main work of this paper is as follows: an iterative reconstruction algorithm with smooth L 0 norm is proposed. An iterative reconstruction algorithm with smooth L0 norm is a low complexity and high accuracy reconstruction method. First of all, on the smooth L0 norm, we sample two functions to approximate the L0 norm and solve the smooth L0 norm problem. The gradient descent method is used to obtain the iterative formula. In each step of iteration, the iterative formula is calculated and the iterative result is obtained. The corresponding support set is obtained, and the iterative result is modified by the support set, which makes the residual error smaller. When the iterative stop condition is reached, the iterative process is stopped. Compared with the contrast algorithm, this method can achieve higher reconstruction accuracy, and its complexity is relatively low. In the case of different sampling rates, the method proposed in this paper has a lower sampling rate when the two-dimensional Lena image is reconstructed. The PSNR of reconstructed signal is obviously higher than that of other contrast algorithms, and it has obvious advantages. An adaptive threshold iterative reconstruction algorithm for distributed compression awareness is proposed. In the network model, a distributed compression sensing signal model is used to model the network model. This method is a decentralized parallel algorithm. Assuming that the nodes in the network have a certain computational power, each node sends its reconstructed support set to the surrounding node, and the node receives the support set of the surrounding node, and fuses the support set to the surrounding node, and finally feeds back to the surrounding node. After many information exchanges, the correct support set can be obtained. This method not only effectively reduces the data transfer in the network, but also uses parallel algorithm, so the reconstruction speed is faster. Experimental results show that the proposed algorithm can reconstruct the original signal perfectly in wireless networks with signal noise.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.7

【参考文献】