基于贝叶斯压缩感知的合成孔径雷达高分辨成像

基于压缩感知(CS)的合成孔径雷达成像方法可以显著减少数据采样时间、数据量以及节省信号带宽。然而,基于CS的方法对噪声和杂波相当敏感,在信噪比较低的时候,成像质量较差。该文结合CS理论提出了合成孔径雷达中的随机孔径贝叶斯压缩感知(BCS)高分辨2维成像方法。在距离向应用CS减少采样数据的同时,在方位向随机抽取部分孔径位置发射和接收信号,以少量的测量孔径和测量数据获得重建目标空间的足够信息。基于贝叶斯的分析方法由于考虑了成像场景中的杂波以及压缩采样过程中的加性噪声,因而能够更好地重建目标空间。仿真结果表明,基于贝叶斯方法得到的图像比基于FFT方法得到的图像更加尖锐,比基于CS方法得到的图像更加稀疏,因而具有更高的分辨率。     

基于贝叶斯假设检验的压缩感知重构

为提高贪婪类算法的重构精度,该文提出一种贝叶斯假设检验匹配追踪算法。该算法首先建立了贝叶斯假设检验模型,用于在噪声污染下识别稀疏信号非零元素的下标;其次利用追踪算法的输出下标集作为该模型的候选集,并对候选集中的每个元素进行假设检验以剔除冗余下标;最后根据剔冗后的真实下标集,采用最小二乘法重构原始信号。仿真结果表明：在相同的实验条件下,与传统贪婪类算法相比,该算法不存在冗余下标,具有更强的抗干扰能力和更高的重构精度。     

基于贝叶斯压缩感知理论的超宽带通信信道估计

超宽带是一种新颖的高速无线通信技术。其过高的带宽给采样带来了困难,压缩感知理论提供了一种可行的低速采样方法。针对目前的压缩感知超宽带信道估计方法必须假设信道稀疏度已知,论文提出了基于贝叶斯压缩感知理论的超宽带信道估计方法。将超宽带信道估计转化为压缩感知理论中的重构问题,并使用贝叶斯压缩感知方法进行重构,得到信道估计值及其误差范围,最终实现信息解调。贝叶斯压缩感知理论将稀疏贝叶斯学习理论引入到压缩感知中,给需要重构向量中的每个值设置受超参数控制的后验概率密度函数,在超参数的更新过程中,零值所对应的超参数将趋向于无穷大,与之对应的后验概率将趋向于零,通过这种方法剔除非重要多径,自适应地找出信道向量中的重要多径,并使用回归算法进行重构。实验结果表明在信道稀疏度未知的情况下,该方法能够对原信道进行有效的重构。     

基于贝叶斯压缩感知的说话人识别方法

说话人识别技术广泛地被应用于互联网和通信领域,近几年,压缩感知理论受到国内外的广泛关注,该理论突破了奈奎斯特采样速率的限制,对可压缩信号在采样的同时也进行压缩,将压缩感知这一新理论与说话人识别这一亟需突破的领域相结合,为说话人识别系统性能的提升带来希望。本文针对与文本无关的说话人识别技术,深入研究了贝叶斯框架下的压缩感知算法,率先提出了基于贝叶斯压缩感知的说话人识别算法;然后针对基于压缩感知的说话人识别算法中的稀疏系数的特点,引入半高斯先验,详细分析基于该先验的贝叶斯压缩感知后,提出基于近似贝叶斯压缩感知的说话人识别算法。     

脉冲超宽带中压缩感知的应用

目前,超宽带(UWB)技术是受到高度重视的一种短距离高速率的无线通信技术,在军事、雷达定位、灾害救援、测距及通信等领域均所应用。然而,由于频谱资源更加珍贵的条件下,使得超宽带无线通信技术的地位越来越重要。脉冲超宽带是其最为经典的实现方式,将压缩感知技术应用到脉冲超宽带中,可有效降低接收机的采样率,具有重要实践意义。     

基于优化信息算子的UWB信道贝叶斯估计

针对压缩感知应用于UWB通信信道估计时信息算子的相干性严重影响UWB信道估计精度的问题,提出将优化的信息算子和贝叶斯算法相结合的方法。该方法以互累积相干参数为准则,首先将加权信息算子通过最优化与正则化得到优化的信息算子,最后通过贝叶斯算法重构UWB信道。理论分析和仿真结果表明优化信息算子的相干性大大减弱,有效提高了UWB信道估计精度,同时该方法能在较低的压缩比和信噪比条件下实现UWB通信信道的准确重建。     

压缩感知的多参数链路故障定位算法

为了提高故障定位性能,降低单一判别参数在单位过程中的约束,该文提出一种基于压缩感知和信息熵差的多参数链路故障定位算法。该算法首先利用贝叶斯网络进行快速故障预测,其次引入参数故障覆盖范围,利用压缩感知进行故障筛选,最后定义参数故障信息熵差完成根源故障定位。仿真结果表明,该算法预测出的故障集合具有可压缩性,筛选后的故障集合保留了真实故障,定位时具有较高的故障检测率和较低的故障误检率。     

基于贝叶斯压缩感知的噪声MIMO雷达稳健目标参数提取方法

针对压缩感知雷达(Compressive Sensing Radar, CSR)面临测量噪声、信道干扰及系统精度误差等扰动时,非自适应随机测量值和感知矩阵失配导致传统CSR目标参数提取性能下降的问题,该文提出一种基于贝叶斯压缩感知(Bayesian Compressive Sensing, BCS)的噪声MIMO雷达稳健目标参数提取方法。文中首先建立了噪声MIMO雷达的稀疏感知模型,推导了基于目标参数稀疏贝叶斯模型的联合概率密度函数,随后将BCS方法与LASSO (Least-Absolute Shrinkage and Selection Operator)算法相结合对联合概率密度函数进行优化求解。与传统CSR算法相比,该方法能够在CSR系统模型存在失配误差时对目标参数进行有效估计,降低了目标参数估计误差,改善了CSR目标参数提取的准确性和鲁棒性。计算机仿真验证了该方法的有效性。     

基于优化贝叶斯压缩感知算法的频谱检测

近年来,压缩感知理论依旧是信号处理领域的研究热点之一。将压缩感知应用于频谱检测技术可以突破传统的奈奎斯特采样定理,降低检测时采样率,因此可以减轻硬件处理的压力。因此适合用在频谱检测技术中,特别是宽带信号的频谱检测。本文对贝叶斯压缩感知理论（BCS,Bayesian Compressed Sensing）进行研究,并将其引入频谱检测技术中。在BCS算法的基础上,通过进一步减小高斯随机观测矩阵列向量的相关度,实现对观测矩阵的优化,得到一种优化的贝叶斯压缩感知算法（称其为OBCS算法,即Optimized BCS）。在MATLAB仿真中,本文提出将数零法作为频谱检测判决规则,并使用BCS和OMP算法作为对照,验证了OBCS算法无论在重构误差、检测概率还是虚警概率等指标上都具有最佳的效果。      

基于贝叶斯压缩感知的ISAR自聚焦成像

针对ISAR自聚焦成像,该文提出一种基于贝叶斯压缩感知的高分辨率成像算法。首先利用目标图像的稀疏特性构建级联形式的稀疏先验模型,同时将相位误差建模为均匀分布模型;然后基于最大后验准则,依据贝叶斯压缩感知理论交替迭代求解目标图像和相位误差。与传统稀疏方法相比,所提算法进一步利用了目标图像的联合稀疏信息,将ISAR CS成像转化为MMV联合稀疏优化问题的求解,可以有效改善自聚焦的精度以及成像质量。仿真结果验证了该算法的有效性。     

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.     

基于压缩感知的定位新型UWB信号抽样方法

Ultra-wide-band (UWB) signals are suitable for localization, since their high time resolution can provide precise time of arrival (TOA) estimation. However, one major challenge in UWB signal processing is the requirement of high sampling rate which leads to complicated signal processing and expensive hardware. In this paper, we present a novel UWB signal sampling method called UWB signal sampling via temporal sparsity (USSTS). Its sampling rate is much lower than Nyquist rate. Moreover, it is implemented in one step and no extra processing unit is needed. Simulation results show that USSTS can not recover the signal precisely, but for the use in localization, the accuracy of TOA estimation is the same as that in traditional methods. Therefore, USSTS gives a novel and effective solution for the use of UWB signals in localization.     

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.     

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.     

Tree-Structured Compressive Sensing With Variational Bayesian Analysis

In compressive sensing (CS) the known structure in the transform coefficients may be leveraged to improve reconstruction accuracy. We here develop a hierarchical statistical model applicable to both wavelet and JPEG-based DCT bases, in which the tree structure in the sparseness pattern is exploited explicitly. The analysis is performed efficiently via variational Bayesian (VB) analysis, and comparisons are made with MCMC-based inference, and with many of the CS algorithms in the literature. Performance is assessed for both noise-free and noisy CS measurements, based on both JPEG-DCT and wavelet representations.     

Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing

Bayesian compressive sensing (CS) is considered for signals and images that are sparse in a wavelet basis. The statistical structure of the wavelet coefficients is exploited explicitly in the proposed model, and, therefore, this framework goes beyond simply assuming that the data are compressible in a wavelet basis. The structure exploited within the wavelet coefficients is consistent with that used in wavelet-based compression algorithms. A hierarchical Bayesian model is constituted, with efficient inference via Markov chain Monte Carlo (MCMC) sampling. The algorithm is fully developed and demonstrated using several natural images, with performance comparisons to many state-of-the-art compressive-sensing inversion algorithms.      

基于贝叶斯压缩感知的复数稀疏信号恢复方法

该文利用复数稀疏信号的时域相互关系提出一种新的稀疏贝叶斯算法(CTSBL)。该算法利用复数信号的实部与虚部分量具有相同的稀疏结构的特点,提升估计信号的稀疏程度。同时将多个测量信号间的内部结构信息引入到了信号恢复中,使原始的多测量稀疏信号恢复问题转变为单测量块稀疏信号恢复问题,使恢复性能得到了提升。理论分析和仿真结果证明,提出的CTSBL算法相较于目前的针对复数信号的多测量矢量贝叶斯压缩感知(CMTBCS)算法和块正交匹配追踪算法(BOMP)在估计精度上具有更好的性能。     

Training Sequence Design for NBI Mitigation in Compressive Sensing UWB Systems

Ultra wideband (UWB) is a promising technology in delivering high data rate for short range wireless communication systems. Because of their large bandwidth, UWB signals may encounter some problems especially with high sampling rate requirements. Moreover, coherence existence with other narrowband systems is a major concern which needs to be addressed through proper mechanisms. The problem becomes so complex if multiple users exist. Since narrowband interference (NBI) signals have sparse representation in the discrete cosine transform (DCT) domain, they can be estimated and suppressed using Compressive Sensing (CS). CS also has the ability to reduce the high sampling rate requirements. For training based NBI mitigation with CS, three groups of pilot symbols are used to estimate the NBI signal subspace, the UWB signal subspace, and to provide information about the channel. In this paper, the distribution of pilot symbols among the three groups is investigated in the presence of strong NBI. The investigation is based on the bit error rate performance and throughput. The influence of each pilot symbols group is studied. The performance is also evaluated in the presence of multiuser interference in addition to the NBI. Simulation results show that the size of the third group of pilot symbols which is used to estimate the channel is the most dominant one.     

基于压缩感知的鲁棒性目标跟踪

压缩感知算法能有效地实时跟踪视频目标,但由于无法对目标特征最优选取,且样本搜索中心由上一帧目标位置所确定,其鲁棒性不高.鉴于此,提出了一种基于压缩感知的改进算法.该算法将meanshift算法与压缩感知算法相结合,从meanshift算法中获得最佳候选区域中心作为压缩感知算法的样本搜索中心,跟踪过程中通过在线特征选择训练的分类器确定最终目标位置.实验表明,改进后的算法不仅在背景干扰大时跟踪精度更高,而且当目标受到遮挡后,也能稳定地跟踪目标.