Bayesian Compressive Sensing

The data of interest are assumed to be represented as N-dimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M Lt N of basis-function coefficients associated with B. Compressive sensing is a framework whereby one does not measure one of the aforementioned N-dimensional signals directly, but rather a set of related measurements, with the new measurements a linear combination of the original underlying N-dimensional signal. The number of required compressive-sensing measurements is typically much smaller than N, offering the potential to simplify the sensing system. Let f denote the unknown underlying N-dimensional signal, and g a vector of compressive-sensing measurements, then one may approximate f accurately by utilizing knowledge of the (under-determined) linear relationship between f and g, in addition to knowledge of the fact that f is compressible in B. In this paper we employ a Bayesian formalism for estimating the underlying signal f based on compressive-sensing measurements g. The proposed framework has the following properties: i) in addition to estimating the underlying signal f, "error bars" are also estimated, these giving a measure of confidence in the inverted signal; ii) using knowledge of the error bars, a principled means is provided for determining when a sufficient number of compressive-sensing measurements have been performed; iii) this setting lends itself naturally to a framework whereby the compressive sensing measurements are optimized adaptively and hence not determined randomly; and iv) the framework accounts for additive noise in the compressive-sensing measurements and provides an estimate of the noise variance. In this paper we present the underlying theory, an associated algorithm, example results, and provide comparisons to other compressive-sensing inversion algorithms in the literature.     

压缩传感技术及其应用

本文综述了一种新的信号处理方法—压缩传感（Compressive Sensing ,CS）,它是针对稀疏或者可压缩信号,在采样的同时即可对信号数据进行适当压缩的新理论。近年来,压缩传感理论成为信号采样及图像处理领域最新、最热点的问题之一。它主要包括三个方面：稀疏表示矩阵,非相干测量矩阵以及重建算法。本文介绍了压缩传感理论的模型,以及压缩传感的主要重建算法,并将实现方法进行了分析与比较。文章最后列举出了压缩传感的主要应用领域。     

Bayesian Compressive Sensing Via Belief Propagation

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(K log(N)) measurements and O(N log²(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.     

Bayesian Compressive Sensing Using Laplace Priors

In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.     

Compressive Sensing [Lecture Notes]

This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. This method, called compressive sensing, employs nonadaptive linear projections that preserve the structure of the signal; the signal is then reconstructed from these projections using an optimization process.     

基于压缩传感的重构算法研究

传统的奈奎斯特采样定理规定采样率必须是频率带宽两倍,浪费大量采样资源。如果信号可以稀疏表示,那么可以采用压缩传感技术重构原始信号,压缩传感能在采样的同时对数据进行适当压缩,节省系统资源。现存的压缩传感重构算法对图像边缘和纹理的重构效果都不太理想,提出一种基于全变差的图像重构算法,该算法能稳定有效地重构图像的边缘和纹理。     

面向内容的语音信号压缩感知研究

压缩感知理论依据信号的稀疏性质进行压缩测量,将信号的获取方式从对信号的采样上升为对信息的感知,是信号处理领域的一场革命。本文提出一种基于非确定基字典（Uncertainty Basis Dictionary, UBD）对语音信号进行稀疏表示的方法,将压缩感知理论应用于对语音信号稀疏表示的压缩,并提出了基于求解线性规划问题的方法重构语音信号的算法。通过语音识别、话者识别和情感识别实验,从面向内容分析的角度,研究这种基于压缩感知理论的信息感知方法是否保留了语音信号的主要内容。实验结果表明,语音识别、话者识别和情感识别的准确率,与目前这些领域研究方法得到的结果基本一致,说明基于压缩感知理论的信息感知方法能够很好地获取语音信号的语义、话者和情感方面的信息。      

压缩感知回顾与展望

压缩感知是建立在矩阵分析、统计概率论、拓扑几何、优化与运筹学、泛函分析等基础上的一种全新的信息获取与处理的理论框架.它基于信号的可压缩性,通过低维空间、低分辨率、欠Nyquist采样数据的非相关观测来实现高维信号的感知.压缩感知不仅让我们重新审视线性问题,而且丰富了关于信号恢复的优化策略,极大的促进了数学理论和工程应用...     

基于感知压缩的探地雷达数据压缩采集

 本文提出一种基于压缩感知的探地雷达数据压缩采集方法,实现实时的采样数据压缩,无需采集完所有数据后再压缩,采样与压缩同时进行,从而大大减小了实时采样的存储压力.探地雷达的采样信号被压缩投影到由Mersenne Twister 算法生成随机矩阵,实现压缩.该方法实现了小计算量的实时压缩,并且硬件实现简单.本文使用half-quadric的方法求解感知压缩模型中的l₁凸优化,快速实现数据重构.实验表明,本文方法能将探地雷达数据压缩把到原来的1/15,大大减小实时采样存储压力.     

用于压缩感知的二值化测量矩阵

压缩感知是近年新兴的一种信号处理理论,在一定条件满足的情况下,压缩感知方法可通过远低于 Nyquist 频率的降采样数据以高概率近乎完美地重建原始信号。测量矩阵在压缩感知的整个处理过程中起着非常重 要的作用。本文从恢复算法入手提出二值化测量矩阵,并通过仿真对其性能加以验证。二值化后测量矩阵不仅在 性能上有一定提升,更重要的是可大大降低测量矩阵所需的存储空间以及压缩感知采样、恢复过程的运算量。     

对比源框架下的多任务贝叶斯压缩感知微波成像方法

针对强散射体微波成像困难问题,本文提出了一种对比源框架下的基于拉普拉斯先验的多任务贝叶斯压缩感知方法,实现了稀疏强散射体的微波成像.在对比源框架下,基于"数据"积分方程并对成像区域网格离散建立稀疏感知模型,前向问题采用矩量法数值模拟;构造基于拉普拉斯先验的贝叶斯压缩感知分层模型;在多入射波情况下,利用多任务贝叶斯压缩感知方法对对比源进行优化求解;最后利用"状态方程"实现了目标函数的重构.本文在考虑噪声情况下,通过对多像素单目标、不均匀目标、多目标的微波成像数值模拟,并与共轭梯度方法、一阶Born近似框架下的多任务贝叶斯压缩感知方法的重构结果比较,验证了本文方法的有效性和鲁棒性.     

High-speed Signal Reconstruction for Compressive Sensing Applications

Compressive sensing (CS) is an emerging technique that has great significance to the design of resource-constrained embedded signal processing systems. However, signal reconstruction remains a challenging problem due to its high computational complexity, which limits the practical application of compressive sensing. In this paper, we propose an algorithmic transformation referred to as Matrix Inversion Bypass (MIB) to reduce the computational complexity of Orthogonal Matching Pursuit (OMP) based signal reconstruction. The proposed MIB transform naturally leads to a parallel architecture for dedicated high-speed hardware implementations. Furthermore, by applying the proposed MIB transform, the energy consumption of signal reconstruction can be reduced as well. This is vital to many embedded signal processing systems that are powered by batteries or renewable energy sources. Simulation results of a wireless video monitoring system demonstrate the advantages of the proposed technique over the conventional OMP-based technique in improving the speed, energy efficiency, and performance of signal reconstruction.

     

压缩感知相移数字全息术

相移数字全息图用传统数字再现可以消除零级像与共轭像,但数字全息术记录的全息图及数字再现像的分辨率被CCD的分辨率所限制.将新兴的压缩感知算法用于数字全息图的稀疏重建,以实现由部分全息图数据得到高分辨率再现像.分析了压缩感知用于重建数字相移全息图的原理,并利用该算法对计算机模拟的相移全息图进行了重建.结果表明,压缩感知算法能够对数字全息图稀疏重建,利用50％的部分全息图数据重建出了较高质量的再现像,并消除了零级像和共轭像.当选用合适的观测器如数字微反射镜器件或随机位相片实现随机观测矩阵时,可以实现单像素成像,从而突破记录全息图CCD分辨率的限制.     

基于能量均衡的无线传感器网络压缩感知算法

无线传感器网络在探测目标源时会碰到处理能力不足和能量缺乏的问题。为了克服这些问题,该文提出了基于能量均衡的自适应压缩感知算法。与传统自适应压缩感知算法不同,所提出的算法在选择观测向量时不仅考虑了重构性能,还考虑了节点的能量均衡,防止某些节点过快消耗能量而导致整体网络结构的破坏。同时为了适应不同应用场景的需求,将自适应压缩感知算法和能量均衡压缩感知算法相结合,通过门限值的选择达到灵活配置的目的。仿真实验的结果表明,该文所提出的算法能够有效延长网络生存时间,同时能够实现能耗和收敛性的兼顾。     

压缩感知的等效二维稀疏变换

目前的压缩感知研究尚不能真正实现基于二维稀疏变换的影像采集和重构。通过对二维压缩感知和稀疏变换的理论分析和数学推导,将基于一维稀疏变换的二维压缩感知模型等价转换成适用于二维稀疏变换的二维压缩感知模型。从而在测量过程不变的前提下,基于一维线阵推扫数据采集方式实现了基于二维稀疏变换的压缩感知影像采集和重构。实验验证了等效二维稀疏变换的正确性。     

压缩感知的重叠神经元峰电位信号分类

随着电生理技术水平的提高,电极可以记录的峰电位信号包含多个神经元峰电位的叠加.本文提出了一种采用压缩感知和最大后验估计的分类算法来解决重叠峰电位分类问题.其中压缩感知算法用于得到稀疏信号,最大后验估计用于搜索出稀疏信号的最优解.在实验中,我们采用仿真和实测的三组数据对本文算法和传统算法进行了测试,实验结果表明,当峰电位波形相似时,相比于k-均值聚类及CBP（Continuous Basis Pursuit）算法,本文算法具有较少的分类错误数.     

超材料压缩感知成像技术

基于超材料和压缩感知理论设计了一套简便的快速成像系统,可用于毫米波及太赫兹(THz)成像,具有结构简单,成像速度快,在不同频段移植性强等优点。系统采用超材料结构互补(CELC)单元设计单通道成像口径,实现了对信息的物理层压缩。基于口径在不同频率辐射特性的不相关性,构造测量矩阵,以扫频方式实现对目标场景的稀疏测量,最后采用两步迭代阈值(TwIST)算法实现对目标场景的重构。已完成K波段、THz波段成像口径设计,以及K波段成像仿真实验,40 cm成像口径理论上具备4.6 cm的距离分辨力和1.3°的角度分辨力。     

基于自适应压缩感知的信道估计算法

传统方法压缩感知算法截取训练序列最后未被数据干扰固定部分作为观测矩阵,该方法为了抵抗最差的信道而浪费了大量的可用观测数据。在此基础上提出了一种自适应压缩感知的信道估计算法,首先对训练序列进行自适应检测,得到整个未受干扰的观测矩阵,再用压缩感知算法计算信道估计。仿真结果表明,这种基于自适应压缩感知的信道估计算法大幅提高了信道估计的准确性。     

无线传感器网络中的分布式压缩感知技术

本文对无线传感器网络中分布式压缩感知的几个关键技术进行了详细阐述。首先,简要论述了压缩感知方法的基本原理;其次,分析了无线传感器网络中的分布式压缩感知技术与单个信号的压缩感知技术的区别,针对无线传感器网络中联合稀疏模型的建立、分布式信源编码以及联合稀疏信号的重构技术等问题进行了详细讨论;分析了在无线传感器网络的实际应用中,联合稀疏模型、分布式信源编码方式及联合稀疏信号重构方法的性能。最后,对无线传感器网络中分布式压缩感知技术的未来研究方向进行了展望。      

基于块压缩感知的SAR层析成像方法

基于压缩感知(Compressive Sensing, CS)的SAR层析成像方法(SAR Tomography, TomoSAR),虽然实现了对目标的3维重构,但对于具有结构特性的目标其重构性能较差。针对这一问题,该文提出了采用块压缩感知(Block Compressive Sensing, BCS)算法,该方法首先在CS方法基础上将具有结构特性的目标信号重构问题转化为BCS问题,然后根据目标结构特性与雷达参数的关系确定块的大小,最后对目标进行块稀疏的l1/l2范数最优化求解。相比基于CS的SAR层析成像方法,该方法更好地利用了目标的稀疏特性和结构特性,其重构精度更高、性能更优。仿真数据和Radarsat-2星载SAR实测数据的试验结果验证了该方法的有效性。