基于1_p范数的压缩感知重构算法及应用研究

发布时间：2018-01-15 15:32

本文关键词：基于1_p范数的压缩感知重构算法及应用研究　出处：《西安电子科技大学》2014年硕士论文　论文类型：学位论文

【摘要】：传统Nyquist采样定理指出：为了不失真的恢复模拟信号，采样频率应该大于或等于模拟信号频谱中最高频率的两倍。高采样率会产生海量数据，其存储和传输是一项艰难的工作，并且产生了大量的冗余数据，会造成资源浪费。近年来提出的压缩感知理论指出：对稀疏或者可压缩信号进行少量非自适应线性投影，投影信号含有足够的信息，从而能对信号进行高概率重建。压缩感知理论的出现改变了先高速率采样然后低码率压缩的信息采集模式，允许采样和压缩同时进行，并且只需采样部分信息，极大地节省了系统资源。本文首先介绍了压缩感知理论，重点介绍了压缩感知重构算法。针对现有的算法应用于图像的重构中时，重构信噪比不高，尤其在与分块思想集合，低采样率时,块效应明显这一缺点，本文提出一种新的基于l p(0p1)范数的将罚函数法与修正Hesse阵序列二次规划方法结合的压缩感知重构算法。将提出的算法用于图像重构,仿真实验表明所提出的新算法可以提高图像恢复精度，在低采样率时，块效应减小，，重构性能明显优于现有的算法。为了更好地实现对压缩感知的实际应用，本文研究了基于压缩感知的麦克风阵列远场声源DOA估计模型。由于麦克风阵列声源DOA估计模型首先满足了压缩感知要求的稀疏性条件，其次，远场声源DOA估计模型中声源到麦克风阵列形成的观测矩阵满足压缩感知测量矩阵的RIP条件。因此，理论上本文提出算法可以用于该模型中，仿真实验也表明，本文提出的基于范数的压缩感知重构算法可以用于远场DOA估计，并且取得了较好的结果。
[Abstract]:The traditional Nyquist sampling theorem points out that in order to recover the analog signal without distortion, the sampling frequency should be greater than or equal to twice of the highest frequency in the analog signal spectrum. It is a difficult task to store and transfer, and it produces a lot of redundant data. The theory of compression perception proposed in recent years points out that a small amount of non-adaptive linear projection is used for sparse or compressible signals, and the projection signals contain sufficient information. The theory of compression sensing changes the information acquisition mode of high rate sampling and then low bit rate compression, which allows sampling and compression to be carried out simultaneously, and only a part of the information needs to be sampled. The system resources are greatly saved. In this paper, we first introduce the theory of compression perception, and focus on the compression perception reconstruction algorithm. When the existing algorithms are used in image reconstruction, the SNR of reconstruction is not high, especially in the set of the idea of block. When the sampling rate is low, the block effect is obvious. In this paper, we propose a new compression perceptual reconstruction algorithm which combines penalty function method with modified Hesse array sequence quadratic programming method based on l p0 p1) norm. The proposed algorithm is used for image reconstruction. Simulation results show that the proposed algorithm can improve the accuracy of image restoration. At low sampling rate, the block effect is reduced, and the reconstruction performance is obviously better than the existing algorithm. In order to realize the practical application of compression perception better. In this paper, the far-field sound source DOA estimation model of microphone array based on compressed sensing is studied. Firstly, the DOA estimation model of microphone array satisfies the sparse condition of compression sensing, and secondly. The observation matrix formed from the sound source to microphone array in the far-field sound source DOA estimation model satisfies the RIP condition of the compressed sensing measurement matrix. Therefore, the algorithm proposed in this paper can be used in the model theoretically. The simulation results also show that the proposed algorithm can be used in far field DOA estimation, and good results are obtained.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

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