1-BIT压缩感知算法及其应用研究

发布时间：2018-01-01 06:35

本文关键词：1-BIT压缩感知算法及其应用研究　出处：《电子科技大学》2016年博士论文　论文类型：学位论文

【摘要】：传统信号处理理论中,采样过程需遵循奈奎斯特(Nyqusit)采样定理,即采样频率至少是信号带宽的两倍,然而,随着信息需求量的日益增加,信号带宽越来越宽,在信息获取过程中对采样速率和数据处理速度提出了越来越高的要求,对相应的硬件设备带来了极大的挑战。由Donoho和Candès提出的压缩感知理论指导下的信号采样率要远远低于Nyquist采样率。在实际系统中,为方便存储和传输,采样数据需要被量化,由此引入了对量化压缩感知的研究,由于1-Bit压缩感知实现方便,受到了极大的关注。当前的1-Bit压缩感知重构算法主要包括固定点延拓算法,匹配符号追踪算法,二元迭代硬门限算法以及其衍生算法。其中,二元迭代硬门限算法性能最优,但是,它要求已知信号的稀疏度,而信号的稀疏度在实际应用中往往是未知量,如何在稀疏度未知的前提下,利用1-Bit采样值有效地重构信号是当前大多数重构算法存在的问题;其次,受噪声的影响,采样数据的符号信息可能发生改变,即出现符号跳变现象,而二元迭代硬门限及其衍生算法不能有效抑制符号跳变的影响,虽然自适应野值追踪技术可以提高其抗符号跳变能力,但是其信号重构性能在符号跳变数较多的情况下会出现较大的衰减,这也是目前1-Bit压缩感知算法存在的一个主要问题。此外,当前大多数1-Bit压缩感知算法都是针对一维信号的重构,很少可以用来快速重构稀疏矩阵。针对这些问题,本文提出了一些相应的算法。论文的主要工作概括如下:针对实际应用中信号的稀疏度未知的问题,本文介绍了两种基于重加权的1-Bit压缩感知方法。这些方法根据信号元素绝对值的不同,给予不同的加权值,通过梯度下降和软门限方法,可以在信号稀疏度未知的条件下,有效重构出原始信号。与现有的算法相比,该算法更适用于实际应用。针对二元迭代硬门限算法不能有效处理符号跳变的问题,本文将1-Bit压缩感知中的信号重构问题看成是分类问题,利用pinball损失函数代替当前算法中的hinge损失函数和线性损失函数,并对pinball损失函数取适当的参数,基于最小化该pinball损失函数的1-Bit压缩感知方法的性能要优于传统的1-Bit压缩感知算法。尤其在符号跳变数量较多的情况下,其性能优势更明显。针对当前1-Bit压缩感知算法只处理稀疏向量的问题,本文提出了一种快速重构稀疏矩阵的1-Bit压缩感知方法,该方法结合了矩阵素描(Matrix Sketching)技术,可以以矩阵的形式重构原始矩阵,缩短了计算时间,也提高了矩阵重构精度。此外,我们将该方法用在图像重构中,利用软门限方法代替原来的硬门限方法。试验结果表明,在相同的测量位数的情况下,该算法的重构性能要优于传统的压缩感知方法。将现有的1-Bit凸优化模型推广到二维的情况,并针对该方法处理符号跳变能力较差的缺点,提出了一种基于最小化pinball损失函数的凸优化模型,并给出了求解该问题的算法。试验结果表明,该算法在符号跳变数量较多的情况下,性能优于传统的方法。
[Abstract]:In the theory of traditional signal processing, the sampling process should follow the Nyquist sampling theorem (Nyqusit), the sampling frequency is at least two times the bandwidth of the signal, however, with the increasing demand, the signal bandwidth is more and more wide, in the process of acquiring information in more and more demands on the sampling rate and the speed of data processing is proposed. Bring a great challenge to the corresponding hardware. Proposed by Donoho and Cand s signal compression perception theory under the guidance of the sampling rate is much lower than the Nyquist sampling rate. In the actual system, for the convenience of storage and transmission, data needs to be quantified, then introduces the research on the quantification of compressed sensing, due to 1-Bit compressed sensing is easy to realize and has attracted great attention. The current 1-Bit compressed sensing reconstruction algorithm mainly includes fixed point continuation algorithm, symbol tracking algorithm, two element iterative hard threshold algorithm And its derivative algorithm. Among them, two yuan of iterative hard threshold algorithm for optimal performance, but it requires a known signal sparsity, and signal sparsity in practical applications is often unknown, how in the premise of unknown sparsity, using 1-Bit sampling signals effectively reconstruction is existed in many reconstruction problems; secondly, under the influence of the noise, sampling data symbol information may change, namely symbol jump phenomenon, while the two element iterative hard threshold and influence derivative algorithm cannot suppress the symbol jump, although adaptive outlier tracking technology can improve the anti symbol jump ability, but the performance of signal reconstruction transitions in the case of many symbols will appear larger attenuation, which is currently one of the main problems in 1-Bit compressed sensing algorithm exists. In addition, most of the current algorithms are 1-Bit compressed sensing needle The reconstruction of one-dimensional signal, rarely can be used to the rapid reconstruction of sparse matrix. To solve these problems, this paper puts forward some corresponding algorithm. The main works are summarized as follows: according to the practical application of the sparse signal of unknown problem, this paper introduces two kinds of heavy weighted 1-Bit method based on compressed sensing. These methods according to the signal the absolute value of different elements, give different weighted values by gradient descent and soft threshold method in the signal sparsity is unknown, effectively reconstruct the original signal. Compared with the existing algorithms, this method is more suitable for practical application. For the two yuan can not effectively deal with the iterative hard threshold algorithm for symbol jump the problem, the problem of signal reconstruction in perceptual 1-Bit compression as a classification problem, using Pinball loss function instead of the current hinge loss function and the loss function of linear loss algorithm And, take appropriate parameters on the pinball performance loss function, minimize the loss function pinball 1-Bit compressed sensing method is superior to the traditional 1-Bit algorithm based on compressed sensing. Especially a large number of symbols in the jump condition, the performance advantage is more obvious. In view of the current 1-Bit compressed sensing algorithm only sparse vector, this paper we propose a fast reconstruction of sparse matrix 1-Bit compressed sensing method, this method combines the matrix sketch (Matrix Sketching) technology, with the original matrix form the reconstruction matrix, shorten the calculation time, but also improve the accuracy of the reconstruction matrix. In addition, we will use this method in image reconstruction, using soft threshold method instead of the original hard threshold method. The experimental results show that the measurement of the same number of bits under the condition that the compressed sensing method to reconstruct the performance of the algorithm is superior to the existing 1-. Bit convex optimization model is extended to two-dimensional case, and the processing method of symbol jump defects of a convex optimization model based on minimizing the pinball loss function, and gives the problem solving algorithm. The experimental results show that the algorithm jump number of symbols in the case of performance superior to the traditional.

【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN911.7

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