压缩感知恢复算法及应用研究

发布时间：2018-08-26 18:58

【摘要】：基于信号的稀疏性结构，集采样和压缩为一体，压缩感知突破了香农采样定理，能够运用远少于香农采样定理所界定的采样数目来精确恢复原始稀疏信号。压缩感知具有广泛的应用背景，包括误差校正、图像处理、通信工程、盲信号分离、模式识别等。压缩感知的研究，促进了信号处理理论和工程应用的发展，已经成为该领域的研究热点之一。信号恢复算法是压缩感知理论的重要组成部分。针对不同的稀疏信号，选择合适的恢复算法，运用尽可能少的测量数目，压缩感知致力于精确恢复原稀疏信号。本文以此为目标，针对恢复算法展开研究，主要贡献如下： 1.基于硬阈值追踪算法（hard thresholding pursuit，HTP），提出了一种新的贪婪算法，旨在解决信号稀疏度未知情况下的恢复性问题。该算法采用了渐近估计稀疏度的技巧，解决真实稀疏度未知造成的困难。将限制等距性质（restricted isometryproperty，RIP）作为理论分析工具，给出了算法收敛的充分条件，并且给出了恢复的信号与原始信号之间的误差上界。在信号稀疏度未知的前提下，合成信号和自然图像的恢复实验表明该算法具有良好的恢复性能。 2.目前，针对块正交匹配追踪算法（block orthogonal matching pursuit，BOMP）精确恢复原始块稀疏信号的条件大多以块-互相关度（block mutual coherence）为判别准则。利用块-RIP，本文给出了保证BOMP算法精确恢复原信号的充分条件，并且说明了给出基于块-RIP的精确恢复条件是必要的；针对人脸识别等工程应用中可能出现冗余块的情况，提出了一种解决冗余块问题的算法，并且给出了保证算法精确恢复的条件；在多重测量向量（multiple measurement vectors，MMV）模型的基础上，本文所提的算法能够实现同时处理多个样本。最后，通过人脸识别的实验，表明了所提算法的有效性。 3.针对所求稀疏信号部分支撑信息已知的情况，提出了加权L2,1最小化方法。该方法可以利用信号序列中帧与帧之间的相关性，，将上一帧的支撑信息作为恢复下一帧信号的先验信息，使得进一步降低采样数目成为可能。利用RIP，给出了恢复的信号与原始信号之间的误差上界。另外，由于该方法将二维的信号直接看做矩阵来处理，而不是将其向量化，这样大大的减少了运行时间。通过恢复Larynx图像序列的实验，验证了算法的有效性。 4.针对贪婪块坐标下降算法（greedy block coordinate descent，GBCD），在加性噪声和乘性噪声干扰下，运用RIP理论工具，分析了该算法的性能。给出了保证GBCD算法精确恢复原始信号的支撑集合的充分条件，并且给出了满足该充分条件的例子；讨论了该充分条件的上界，通过例子，指出了在不满足该充分条件时，存在着GBCD算法不能精确恢复的情况。最后，通过仿真实验，验证了GBCD算法的性能。
[Abstract]:Based on the sparse structure of signal, which integrates sampling and compression, the compression perception breaks through the Shannon sampling theorem, and it can accurately restore the original sparse signal by using the number of samples defined by Shannon sampling theorem, which is far less than the number of samples defined by Shannon sampling theorem. Compression sensing has a wide range of applications, including error correction, image processing, communication engineering, blind signal separation, pattern recognition and so on. The research of compression sensing, which promotes the development of signal processing theory and engineering application, has become one of the research hotspots in this field. Signal recovery algorithm is an important part of compression perception theory. For different sparse signals, the appropriate restoration algorithm is selected, and the number of measurements is as small as possible. The compression sensing is devoted to the accurate restoration of the original sparse signals. In this paper, the main contributions of this paper are as follows: 1. Based on the hard threshold tracking algorithm (hard thresholding pursuit,HTP), a new greedy algorithm is proposed to solve the recovery problem with unknown signal sparsity. The algorithm uses the technique of asymptotic estimation of sparsity to solve the difficulty caused by unknown real sparsity. Using the restricted equidistant property (restricted isometryproperty,RIP) as a theoretical analysis tool, the sufficient conditions for the convergence of the algorithm are given, and the upper bound of the error between the recovered signal and the original signal is given. Under the condition that the signal sparsity is unknown, the experimental results of synthetic signal and natural image show that the algorithm has good recovery performance. 2. At present, for block orthogonal matching tracking algorithm (block orthogonal matching pursuit,BOMP), most of the conditions for accurate restoration of original block sparse signals are based on block-mutual correlation degree (block mutual coherence) criteria. By using block -RIPs, this paper gives sufficient conditions to guarantee the accurate restoration of original signals by BOMP algorithm, and explains the necessity of giving accurate restoration conditions based on block -RIP, aiming at the possible occurrence of redundant blocks in engineering applications such as face recognition. This paper proposes an algorithm to solve the redundant block problem, and gives the conditions to ensure the accurate recovery of the algorithm. On the basis of the multi-measurement vector (multiple measurement vectors,MMV) model, the algorithm proposed in this paper can process multiple samples at the same time. Finally, the experiments of face recognition show that the proposed algorithm is effective. In this paper, a weighted L _ 2N _ 1 minimization method is proposed to minimize the partial support information of the sparse signal. This method can take advantage of the correlation between frame and frame in the signal sequence and use the support information of the previous frame as the prior information of the signal of the next frame, which makes it possible to further reduce the number of samples. The error upper bound between the recovered signal and the original signal is given by using RIP,. In addition, because the two-dimensional signal is treated as matrix instead of vectorization, the running time is greatly reduced. The effectiveness of the algorithm is verified by the experiment of restoring Larynx image sequence. 4. 4. Aiming at the greedy block coordinate descent algorithm (greedy block coordinate descent,GBCD), the performance of the algorithm is analyzed by using RIP theory under additive noise and multiplicative noise interference. A sufficient condition is given to guarantee the accurate restoration of the support set of the original signal by the GBCD algorithm, and an example of satisfying the sufficient condition is given, the upper bound of the sufficient condition is discussed, and it is pointed out that if the sufficient condition is not satisfied, There exists the situation that the GBCD algorithm can not recover accurately. Finally, the performance of GBCD algorithm is verified by simulation experiments.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.7

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