压缩感知块稀疏信号重构算法研究

发布时间：2018-06-25 12:29

本文选题：压缩感知 + 块稀疏信号　；参考：《湘潭大学》2014年硕士论文

【摘要】：近年来，压缩感知（Compressed Sensing,CS）理论的研究受到越来越多学者的关注，它突破了信号处理领域中传统的香农/奈奎斯特（Shannon/Nyquist）采样定理的采样限定，大大降低了采样数据量，在医学影像、图像处理、雷达探测、模式识别等领域得到了广泛的应用。压缩感知理论的一个重要任务是对压缩采样后的信号进行重构，这些信号都是稀疏或可稀疏化的，即信号中只有少量元素是非零的，且非零元素的位置是随机的。但是实际中大部分信号具有一定的内在结构，，近几年非零元素成块出现的块稀疏信号成为压缩感知理论的研究热点。本文从压缩感知理论出发，对压缩感知块稀疏信号重构算法进行了研究。我们首先详细介绍了标准块稀疏信号重构算法混合l2/l1范式最小化问题（Mixedl2/l1NormOptimization Program,L-OPT）、块匹配追踪算法（Block matching pursuit,BMP）、块正交匹配追踪（Block orthogonal matching pursuit, BOMP）算法。通过对标准的块稀疏信号的重构算法进行分析讨论，我们对当前广泛使用的块正交匹配追踪算法的若干不足进行改进，提出了三个改进的块正交匹配追踪算法，分别为基于前向预测策略的块正交匹配追踪算法（LABOMP）、基于正交投影的块正交匹配追踪算法（PBOMP）以及结合前两者提出的改进算法（PLABOMP）。其中LABOMP算法是针对BOMP算法在迭代选择原子块的过程中，每次选择当次迭代最优的原子块，并不能保证最终迭代性能是最优的问题，提出的在每次迭代过程中通过预测原子块在未来迭代过程中的性能来选择最优原子块的算法；PBOMP算法是针对运用内积准则选择原子块的算法得不到最优原子块的缺陷，提出的运用正交投影策略来选择更加适宜的原子块的算法；PLABOMP算法是结合前两者平衡时间复杂度和精度的改进算法。通过对比实验可知，本文提出的若干算法较BOMP算法在精度和复杂度方面均有所改进。块稀疏重构算法中没有一种权威的算法能保证重构精度、时间复杂度等性能都优于其他算法。本文针对各种块稀疏重构算法的不足，提出了基于融合的块稀疏重构算法（BlockFA），该算法将参与融合的各个算法得到的信号估计进行融合得到最后的估计信号。其主要优势在于参与融合的每个算法都无需任何较大的修改就能进行，且结合了现有不同的块稀疏重构算法的优势，得到新的重构算法的重构精度不低于任何参与融合的算法。
[Abstract]:In recent years, the research of compressed sensing CS (CS) theory has been paid more and more attention by more and more scholars. It breaks through the sampling limitation of the traditional Shannon / Nyquist sampling theorem in the field of signal processing, and greatly reduces the amount of sampling data in medical images. Image processing, radar detection, pattern recognition and other fields have been widely used. One of the important tasks of compression sensing theory is to reconstruct the compressed sampled signals, which are sparse or sparse, that is, only a few elements in the signal are non-zero, and the position of the non-zero elements is random. However, most of the signals have a certain internal structure in practice. In recent years, block sparse signals with non-zero elements have become the research focus of compression sensing theory. Based on the theory of compressed sensing, the algorithm of sparse signal reconstruction of compressed perceptual blocks is studied in this paper. We first introduce the standard block sparse signal reconstruction algorithm, the mixed l2/l1 normal minimization problem (Mixedl2 / L1 Norm Optimization Programms-OPT), the Block matching tracking algorithm (BMP), and the Block orthogonal matching pursuit, tracking (BMP) algorithm. Through the analysis and discussion of the standard block sparse signal reconstruction algorithm, we improve some shortcomings of the current block orthogonal matching tracking algorithm, and propose three improved block orthogonal matching tracking algorithms. They are block orthogonal matching tracking algorithm (LABOMP) based on forward prediction strategy, block orthogonal matching tracking algorithm (PBOMP) based on orthogonal projection and improved algorithm (PLABMP) combined with the former two algorithms. The LABOMP algorithm can not guarantee that the final iteration performance is optimal when selecting the best atomic block in the process of iterative selection of atomic block. The algorithm proposed to select the optimal atomic block in each iteration process by predicting the performance of atomic block in the future iteration process is aimed at the defect that the algorithm using the inner product criterion to select the atomic block can not get the optimal atomic block. The proposed algorithm, which uses orthogonal projection strategy to select more suitable atomic blocks, is an improved algorithm which combines the former two algorithms to balance time complexity and precision. The comparison experiments show that the proposed algorithms are better in accuracy and complexity than the BOMP algorithm. There is no authoritative algorithm in block sparse reconstruction algorithm which can guarantee the reconstruction accuracy and time complexity. In this paper, a block sparse reconstruction algorithm based on fusion (BlockFA) is proposed to overcome the shortcomings of various block sparse reconstruction algorithms. Its main advantage is that each algorithm involved in the fusion can be implemented without any big modification, and combining the advantages of the existing block sparse reconstruction algorithm, the reconstruction accuracy of the new reconstruction algorithm is no less than that of any other fusion algorithm.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.7

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