【作者】 曾辉；

【导师】 高协平；

【作者基本信息】 湘潭大学 ， 计算机科学与技术， 2014， 硕士

【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。更多还原

【Abstract】 In recent years, Compressed Sensing (CS) theory has attracted wide attention ofresearchers. It breaks through the limitations of traditional Shannon/Nyguist samplingtheorem in the field of signal processing, and greatly reduces the sampling requirements. Ithas been widely used in medical imaging, image processing, radar detection, patternrecognition, etc. Signal reconstruction is an important part of Compressed Sensing theory, butthe premise of signal reconstruction based on Compressed Sensing is that the signal is sparseor it can be converted to sparse signal. Sparse signal is a kind of signal that has only littlenonzero entries and the locations of the nonzero entries are random. Actually, most of thesparse signal has intrinsic structure. Recently, block sparse signal with nonzero entriesappeared in clusters has been a hot area of research.From the theory of compressed sensing, we have done intense research on block sparsesignal reconstruction algorithm. First we have introduced three widely studied block sparsesignal reconstruction algorithm which are the mixedl2/l1Norm Optimization Program(L-OPT), the block matching pursuit (BMP) and the block orthogonal matching pursuit(BOMP). The block orthogonal matching pursuit algorithm has been widely used for blocksparse signal in the reconstruction of compressed sensing. Then in this paper we haveproposed three new algorithms for improving the performance of the block orthogonalmatching pursuit algorithm. They are block orthogonal matching pursuit algorithm based onlook ahead strategy (LABOMP), block orthogonal matching pursuit algorithm based onorthogonal projection (PBOMP) and new algorithm combined them (PLABOMP). Theselection of atoms are vital for the BOMP algorithm, however the outcome of BOMPalgorithm maybe not optimum because it only chooses the local optimum atom in eachiteration. For LABOMP algorithm, the selection of atoms in the current iteration depend on itseffect on the future iterations, it provides a better performance. For the standard BOMP, theinner product is used to select a block of atom in each iteration which can’t get the mostcorrelated atoms. For PBOMP algorithm, a set of potential atoms are chosen and then a singleblock is finally selected based on orthogonal projection. PLABOMP is an algorithm combinesLABOMP and PBOMP algorithms such that a trade off between computational complexityand reconstruction performance can be established. Experiment has shown that the proposedthree new algorithms in this paper perform much better than BOMP algorithm for the signalto reconstruction noise ratio and time complexity.It has been observed that none of the block sparse signal reconstruction algorithmsoutperforms all others in the reconstruction performance and computational complexity. For this problem, we propose a fusion algorithm for block sparse signal reconstruction algorithm(BlockFA). It uses all viable algorithms and fuses their output sparse signal estimates todetermine a final signal estimate. The main advantage of BlockFA is that the participatingalgorithms need not require any modification and we can gain more reliable information thanthe information gained from each participate algorithm. Through experiment comparision, wefind that the proposed algorithm achieve a better reconstruction performance than anyparticipating algorithm.更多还原