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。      

改进的多原子匹配追踪算法处理FBG信号

针对光纤布拉格光栅(FBG)传感信号难以去除噪声 干扰及信号丢失问题,采用压缩感知(CS)对传感信号进行处理。CS 重构算法多是 以稀疏度已知为 先验条件,提出稀疏度确定方法,结合二次正交匹配追踪(TOMP)算法和广义正交匹配追踪(G OMP)算法提出广义二次正交匹配追踪 (GtOMP)算法,确定每次迭代选择原子个数及迭代次数。 首先计算相关系数,归一化后按降序排列,并结合饱和值的方法确定稀疏度,利用平稳度找 出每次迭代所 选择的原子个数,最后利用本文方法对FBG信号进行重构。实验仿真表明,与同类的TOMP 算法相比,本 文算法不仅运行时间大大减少,而且降低了6~20%的重构误差;与其 他不同类算法相比,本 文算法重构信号的信噪比(SNR)提高27dB以上。     

一种基于能量的压缩感知稀疏度估计算法

压缩感知理论中,信号稀疏度直接关系到采样速率的设定以及观测矩阵的构造,而该先验信息往往受限.针对这一问题,本文从大维随机矩阵谱分析理论出发,分析了采样协方差矩阵的极限特征值概率分布特征,并结合其与观测信号能量的关系推导得到观测信号能量与压缩率、稀疏度和信噪比之间的对应关系,提出一种基于观测信号能量的稀疏度估计算法.相对于已有算法,该算法计算复杂度较低,且估计精度较好,并可通过增加采样开销进一步提升稀疏度估计精度,仿真实验验证了本文算法的有效性.     

MR image reconstruction from highly undersampled k-space data by dictionary learning

Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.     

基于改进正交匹配追踪的FBG传感信号处理方法

针对光纤布拉格光栅(FBG)传感信号易受外界噪声干扰从而导致信号丢失的问题,提出了一种改进型正交匹配追踪(OMP)算法。围绕FBG传感信号波长随应力漂移的本质特征,在压缩感知理论的框架下,通过去除稀疏系数中的虚部,并利用指数饱和法对非零元素进行拟合与排序,从而获取FBG信号的有效稀疏度。在此基础上,通过改进经典OMP算法迭代过程中的原子选择策略与终止条件,有效降低算法复杂度并提高信号的重构精度。对比实验结果表明,所提出的算法在时间复杂度、信噪比与信号重构精度等方面均具有突出的优势。     

面向压缩感知的块稀疏度自适应迭代算法

块稀疏信号是一种典型的稀疏信号,目前在块稀疏信号的压缩感知问题中,大多数信号重构算法要求信号的块稀疏度已知且算法复杂度高.针对实际应用中信号块稀疏度未知的情况,提出了一种块稀疏度自适应迭代算法,用于信号重构.首先,该算法初始化一个块稀疏度,其值按设定步长进行增加.对每一个块稀疏度的迭代,算法都会找到信号支撑块的一个子集,并修正更新上一次找到的信号支撵块,最后找到信号的整个支撑块,从而重构出源信号.该算法不需要信号的块稀疏度作为先验知识,而且算法复杂度低.仿真实验表明,该算法的重构概率较已有大多数块稀疏信号重构算法的重构概率高,在块稀疏信号的压缩感知问题中具有实际意义.     

A distributed compressed sensing approach for speech signal denoising

Compressed sensing, a new area of signal processing rising in recent years, seeks to minimize the number of samples that is necessary to be taken from a signal for precise reconstruction. The precondition of compressed sensing theory is the sparsity of signals. In this paper, two methods to estimate the sparsity level of the signal are formulated. And then an approach to estimate the sparsity level directly from the noisy signal is presented. Moreover, a scheme based on distributed compressed sensing for speech signal denoising is described in this work which exploits multiple measurements of the noisy speech signal to construct the block-sparse data and then reconstruct the original speech signal using block-sparse model-based Compressive Sampling Matching Pursuit (CoSaMP) algorithm. Several simulation results demonstrate the accuracy of the estimated sparsity level and that this denoising system for noisy speech signals can achieve favorable performance especially when speech signals suffer severe noise.     

基于非局部相似性和交替迭代优化算法的图像压缩感知

压缩感知理论突破了信号带宽对奈奎斯特采样定理的限制,并且实现了在数据采样的同时进行压缩。目前压缩感知系统通常利用图像在某个变换域具有稀疏性的先验知识,从少量观测值中重构原始图像。本文利用图像像素的邻域结构信息及图像子块的相似性,将图像的非局部相似性作为先验知识运用到压缩感知图像重构中。结合图像的非局部相似性及其在变换域的稀疏性先验知识,提出了基于非局部相似性和交替迭代优化算法的图像压缩感知重构算法,该算法利用迭代阈值法和非局部全变差来交替迭代求解变换域的稀疏性优化问题和非局部相似性的优化问题。实验结果表明,本文算法可以有效提高图像重构的视觉效果和峰值信噪比。      

帧间自适应压缩感知算法在视频编码中的应用

阐述了压缩感知的理论框架,分析了视频信号帧间相关性特点,提出了一种帧间自适应压缩感知的视频编码算法。本方法中,利用视频差值信号的特点建立自适应感知模型,自适应的选择稀疏域和重构域对信号进行压缩感知恢复,在空域稀疏度较强的情况下选择空域作为稀疏域和重构域,在空域稀疏度较差的情况下选择小波域作为稀疏域和重构域。用测试视频进行了仿真分析,结果表明该算法能够取得较好的效果。     

基于低秩稀疏约束的穿墙雷达成像算法

针对穿墙雷达(TWR)成像过程中墙杂波与成像空间分别具有低秩性和稀疏性的特点,提出了一种基于低秩稀疏约束的穿墙雷达成像算法.所提成像算法通过奇异值软阈值法和l1范数最小化技术进行迭代求解低秩稀疏约束优化问题,实现在墙体强反射波存在的探测环境中基于压缩感知框架对墙后隐蔽目标的准确成像重建.仿真和实验数据的处理结果验证了所提成像算法的有效性和准确性.     

一种用于图像重构的新型贝叶斯压缩感知技术

近几年来,贝叶斯压缩感知（BCS）技术得到了快速的发展并逐渐成为压缩感知领域的一项主流技术。该技术主要针对压缩感知中的重构部分,与传统的重构算法不同,其应用的是贝叶斯概率模型,而不是传统的1范数最小化模型。BCS的核心是相关向量机（RVM）,但是,应用传统的RVM进行信号重构往往精度非常差。为了提高精度,文中提出了一种新的BCS技术：粒子群贝叶斯压缩感知（PSBCS）。实验表明这种新的BCS技术在重构精度上大大超越了传统的BCS技术。     

A generalization of the two-dimensional prolate spheroidal wave function method for nonrectilinear MRI data acquisition methods.

The two-dimensional (2-D) prolate spheroidal wave function (2-D PSWF) method was previously introduced as an efficient method for trading off between spatial and temporal resolution in magnetic resonance imaging (MRI), with minimal penalty due to truncation and partial volume effects. In the 2-D PSWF method, the k-space sampling area and a matching 2-D PSWF filter, with optimal signal concentration and minimal truncation artifacts, are determined by the shape and size of a given convex region of interest (ROI). The spatial information in the reduced k-space data is used to calculate the total image intensity over a nonsquare ROI instead of producing a low-resolution image. This method can be used for tracking dynamic signals from non-square ROIs using a reduced k-space sampling area, while achieving minimal signal leakage. However, the previous theory is limited to the case of rectilinear sampling. In order to make the 2-D PSWF method more suitable for dynamic studies, this paper presents a generalized version of the 2-D PSWF theory that can be applied to nonrectilinear data acquisition methods. The method is applied to an fMRI study using a spiral trajectory, which illustrates the methods efficiency at tracking hemodynamic signals with high temporal resolution.     

采用压缩感知的标准测控信号处理

针对测控通信信号接收端存在数据大量冗余的问题,利用标准测控信号在频域上的稀疏性,采用压缩感知的理论进行前期处理。分别考虑了只存在测距音、只存在遥测信号和两类信号都存在等三种条件下的信号处理问题。通过改变稀疏度的大小,可以在不影响解调性能的条件下,大幅度降低接收端所需要的采样率,并且达到消除系统中不需要的谐波的目的。仿真验证了方法的有效性,同时说明利用压缩感知技术,将为测控通信系统的射频直接采样和处理提供一种高效的方式。     

基于二项分布改进的宽带压缩频谱检测方案

宽带压缩频谱检测存在依赖稀疏度先验信息和信号重构时延较高的问题.因此,本文提出了一种高效可靠的宽带压缩频谱检测方案.首先,推导出了基于二项分布精确置信区间改进的稀疏度估计模型.其次,利用稀疏度估计上下界改进了稀疏度自适应匹配追踪算法.最后,提出了一种宽带压缩频谱检测方案.仿真结果表明,本文所提出方法可以同时精确的估计信号稀疏度的上下界,提高了频谱检测的效率和可靠性,加快了算法的收敛速度.     

基于压缩感知的信号重构研究

按照Nyquist采样定理,信号的采样率必须为信号最高频率的2倍以上,这会产生大量的冗余数据。压缩感知是一种新兴的采样理论,对于可以稀疏表示的信号,它能够以远低于Nyquist采样速率对信号进行采样,并通过优化算法实现重构。介绍了压缩感知的基本理论,并分别选取时域稀疏、频域稀疏和图像信号进行了仿真分析,实验结果显示,压缩感知理论能较好的重构原始信号。     

Bayesian compressive sensing using reweighted laplace priors

Bayesian compressive sensing (BCS) plays an important role in signal processing for dealing with sparse representation related problems. BCS utilizes a Bayesian model to solve the compressing sensing (CS) problem, such as signal sampling processing and model parameters using the hierarchical Bayesian framework. The use of Gaussian and Laplace distribution priors on the basic coefficients has already been demonstrated in previous works. However, the two existing priors cannot more effectively encode sparsity representation for unknown signals. In this paper, a reweighted Laplace distribution prior is proposed for hierarchical Bayesian to fully exploit the sparsity of unknown signals. The proposed algorithm can automatically estimate all the coefficients of unknown signal, and the expected model parameters are solely gotten from observation by developing a fast greedy algorithm to solve the Bayesian maximum posterior and type-II maximum likelihood. Theoretical analysis on the sparsity of the proposed model is analyzed and compared with the Laplace priors model. Moreover, numerical experiments are conducted to prove that the proposed algorithm can achieve superior performance for reconstructing unknown sparse signal with low computational burden as well as high accuracy.     

Compressive slow-varying wideband power spectrum sensing for cognitive radio

Wideband spectrum sensing is a critical component of a functioning cognitive radio system. Its major challenge is the too high sampling rate requirement. Compressive sensing (CS) promises to be able to deal with it. Nearly all the current CS-based compressive wideband spectrum sensing methods exploit only the frequency sparsity to perform. This paper sets up a new signal model which is sparse in both temporal and frequency domain. Motivated by the achievement of a fast and robust detection of the wideband spectrum change, total variation minimization is incorporated to exploit the temporal and frequency structure information to enhance the sparsity level. As a sparser vector is obtained, the spectrum sensing period would be shortened and sensing accuracy would be enhanced. Both theoretical analysis and numerical experiments demonstrate the performance improvement.     

自适应稀疏度的1 bit压缩重构算法

1 bit压缩感知技术日益受到关注.1 bit信号往往有符号跳变,同时信号重构还需要稀疏度先验信息,如何有效地克服信号重构对稀疏度的依赖性,提高重构算法对噪声的鲁棒性,这是该领域面临的重大挑战.本文在二进制迭代硬阈值算法基础上,引入自适应稀疏度,利用残差能量的大小,通过对信号和噪声的学习,解决稀疏度依赖问题,通过引入弹...     

Augmented Lagrangian based reconstruction of non-uniformly sub-Nyquist sampled MRI data

MRI has recently been identified as a promising application for compressed-sensing-like regularization because of its potential to speed up the acquisition while maintaining the image quality. Thereby non-uniform k-space trajectories, such as random or spiral trajectories, are becoming more and more important, because they are well suited to be used within the compressed-sensing (CS) acquisition framework. In this paper, we propose a new reconstruction technique for non-uniformly sub-Nyquist sampled k-space data. Several parts make up this technique, such as the non-uniform Fourier transform (NUFT), the discrete shearlet transform and a augmented Lagrangian based optimization algorithm. Because MRI images are real-valued, we introduce a new imaginary value suppressing prior, which attenuates imaginary components of MRI images during reconstruction, resulting in a better overall image quality. Further, a preconditioning based on the Voronoi cell size of each NUFT data point speeds up the conjugate gradient optimization used as part of the optimization algorithm. The resulting algorithm converges in a relatively small number of iterations and guarantees solutions that fully comply to the imposed constraints. The results show that the algorithm is applicable not only to sub-Nyquist sampled k-space reconstruction, but also to MR image fusion and/or resolution enhancement.     

基于分治试探的盲自适应匹配追踪重构算法

压缩感知是一种针对稀疏可压缩信号进行压缩采样的信号处理新方法,针对现有稀疏度探测方法中探测次数较多的问题,基于分治思想提出了盲稀疏度自适应匹配追踪（BSAMP）算法,首先分治试探信号稀疏度,使得其估计值快速逼近真实值,然后通过自适应分组并扩充信号支撑域的方法,快速筛选出有效支撑,并通过弱匹配剪枝得到重构信号。可以在信号稀疏度未知的情况下,快速估计出信号的稀疏度并精确重构出原信号。仿真实验表明：在相同条件下,该算法的重构时间比其他同类算法短,且重构概率也大于其他同类算法。