基于压缩感知的图像采集及重构算法研究

发布时间：2018-06-07 12:58

本文选题：压缩感知 + 测量矩阵　；参考：《湖南师范大学》2014年硕士论文

【摘要】：用远低于尼奎斯特频率的采样速率来收集信号,并在接收端通过相应的恢复算法完成对原始信号精确重构的压缩感知作为一个全新的信息获取及处理的理论框架,打破了传统的尼奎斯特香农采样理论,成为信号处理各个领域的热点。本文在国内外研究的基础上,从分析压缩感知理论的基本原理出发,对基于压缩感知的图像采集及重构算法进行了详细研究。从构造合适的确定性测量矩阵以及提高图像重构算法精度等方面入手,重点研究了常用的测量矩阵、贪婪追踪算法等内容。论文主要贡献有以下几个方面：第一,给出了基于低密度奇偶校验矩阵的确定性测量矩阵。针对目前常用的随机测量矩阵计算复杂度高、需要的存储空间大以及硬件上不易实现的缺点,考虑低密度奇偶检查码编解码与压缩感知理论之间的相似性,提出将Gallager构造的阶梯校验矩阵作为测量矩阵应用于压缩感知。此外,结合PEG算法和准循环构造法,构造一种基于PEG算法的准循环测量矩阵。两种新的测量矩阵在相关性和Gram矩阵非对角线上最大元素值几个衡量参数上都要优于现有的常用测量矩阵,需要的存储空间小,便于硬件的实现。第二,给出了一种自适应前瞻子空间追踪算法。该算法针对子空间追踪算法每次迭代固定的引入内积最大的K个原子加入候选集所引起的误差,引进前瞻策略和自适应选择步长的方法,既保证了提高信号重构的精度又平衡了重构所需的时间。通过Matlab软件对上述提出的测量矩阵以及算法进行仿真实验,分析实验结果,验证了提出来的测量矩阵在性能上优于现在常用的测量矩阵,改进的重构算法相比其他的贪婪追踪算法在一维信号和二维图像重构上也具有一定的优越性。
[Abstract]:The signal is collected at a rate far below the Nyquist frequency, and the compression perception of the accurate reconstruction of the original signal is accomplished by the corresponding recovery algorithm at the receiving end as a new theoretical framework for information acquisition and processing. It breaks the traditional Nyquist Shannon sampling theory and becomes a hot spot in all fields of signal processing. Based on the research at home and abroad, the image acquisition and reconstruction algorithm based on compression perception is studied in detail, based on the analysis of the basic principle of compression perception theory. From the aspects of constructing suitable deterministic measurement matrix and improving the precision of image reconstruction algorithm, the common measurement matrix and greedy tracking algorithm are studied emphatically. The main contributions of the thesis are as follows: First, the deterministic measurement matrix based on low density parity check matrix is given. In view of the high computational complexity, the large storage space and the difficulty in hardware implementation of the random measurement matrix, the similarity between the low density parity check code coding and decoding and the compression sensing theory is considered. The step check matrix constructed by Gallager is applied to compression sensing as a measurement matrix. In addition, combined with PEG algorithm and quasi-cyclic construction method, a quasi-cyclic measurement matrix based on PEG algorithm is constructed. The two new measurement matrices are superior to the existing measurement matrices in terms of the correlation and the maximum element value on the non-diagonal Gram matrix. The storage space is small and the hardware is easy to implement. Secondly, an adaptive prospective subspace tracking algorithm is presented. Aiming at the errors caused by the introduction of K atoms with the largest inner product into the candidate set in each iteration of the subspace tracking algorithm, the forward looking strategy and the adaptive selection of step size are introduced. It can not only improve the precision of signal reconstruction, but also balance the time needed for reconstruction. The proposed measurement matrix and algorithm are simulated by Matlab software, and the experimental results are analyzed. The performance of the proposed measurement matrix is better than that of the commonly used measurement matrix. Compared with other greedy tracking algorithms, the improved reconstruction algorithm also has some advantages in one dimensional and two dimensional image reconstruction.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.73

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