一种用于压缩感知理论的投影矩阵优化算法

考虑到投影矩阵对压缩感知(CS)算法性能的影响,该文提出一种优化投影矩阵的算法。该方法提出可导的阈值函数,通过收缩Gram矩阵非对角元的方法压缩投影矩阵和稀疏字典的相关系数,引入基于沃尔夫条件(Wolfes conditions)的梯度下降法求解最佳投影矩阵,达到提高投影矩阵优化算法稳定度和重构信号精度的目的。通过基追踪(BP)算法和正交匹配追踪(OMP)算法求解l0优化问题,用压缩感知方法实现随机稀疏向量、小波测试信号和图像信号的感知和重构。仿真实验表明,该文提出的投影矩阵优化算法能较大地提高重构信号的精度。     

基于矩阵分解的压缩感知算法研究

奈奎斯特采样定律是长久以来具有指导意义的经典信号处理技术,它提出信号在采样过程中,当且仅当采样率大于信号带宽的2倍时,才能精确重构信号。压缩感知理论突破了奈奎斯特采样定理对信号采样率的限制,以更低采样率采样信号,并通过适当的重构算法恢复信号。文中以压缩感知理论为基础,结合目前广泛采用的正交匹配追踪算法,基于矩阵分解思想,提出2种改进算法,在运算复杂度方面取得优化,并且满足信号处理时对重构精度的要求。     

一种改进的压缩感知重构算法研究

主要研究重构算法的贪婪算法中的正交匹配追踪算法,并提出了基于正交匹配追踪算法的改进算法,对图像进行列变换后,再对原图像进行行变换,然后综合两幅图像的优点,重构出原图像.仿真结果表明这种改进的算法能够有效地提高重构效果.     

基于压缩感知理论的图像重构技术

通过CS理论在工程应用上典型的正交匹配追踪算法,实现了一维信号和二维图像的精确重构,针对该方法中出现对整幅图像进行采样计算时需要大量的观测矩阵存储空间,并且重构过程中耗费了大量的时间等问题,提出了一种基于OMP算法的改进方案,将图像进行分块压缩感知。通过实验分析,以上问题得到了解决,重构图像的质量在没有增加计算复杂度的前提下也得到了提高。     

一种基于正交匹配追踪的压缩感知信号检测算法

针对当前压缩感知信号检测算法没有充分利用稀疏系数幅值信息的不足,提出了一种新的检测算法。从正交匹配追踪算法切入,通过深入分析归一化残差的变化信息,提出归一化余差概念,建立了一种基于归一化残差和归一化余差二维判决的信号检测算法。仿真结果表明,算法的有效检测阈值区间随着信噪比的降低而不断减小,且在信噪比为-8 dB、压缩比为0.25时,该算法的检测概率仍能满足要求,具备较好的适应性。     

前视SAR压缩感知成像算法

以进一步提高前视SAR成像的分辨率为目的,提出了一种基于压缩感知的前视SAR成像算法。前视SAR是一种可以实现对飞行路线正前方的区域进行成像的工作模式,通过分析德国宇航局提出的前视SAR系统——视景增强的新型区域成像雷达(SIREV)可知,由于SIREV系统天线长度的限制,使得等效的合成孔径长度较短,从而导致成像的分辨率较低。而基于压缩感知的前视SAR成像算法可以在方位向等效得到一个较长的虚拟天线,因此可以在同样长度天线的情况下获得更高的成像分辨率。仿真结果表明,该方法可以实现对点目标、分布目标和面目标的成像,并且提高了成像的分辨率。     

LTE-A基于压缩感知的信道估计

针对在多普勒环境下LTE-A(改进的长期演进)系统时频域二维稀疏信道的特性,根据导频在时频域的分布以及二者之间的相关性,通过将搜索空间分解为时域上OFDM(正交频分复用)符号间和频域上子载波间范围,提出了一种基于OMP(正交匹配追踪)算法改进压缩感知的信道估计。仿真结果表明,改进的OMP算法较原始算法具有更低的MSE(均方误差)。     

基于压缩感知OMP改进算法的图像重构

正交匹配追踪(OMP)算法中迭代次数严格依赖信号的稀疏度K值,迭代次数选取适当会重构出高精确的图像,反之则会对图像重构质量造成严重影响.针对这一问题,提出了一种根据残差值的相对极差来确定最佳迭代次数的新方法.该方法要求在同一次迭代中对一幅图像的所有列同时进行迭代计算,根据极差的相对差值与门限值比较来确定最佳迭代次数,从而达到提高重构精度,消除对稀疏度K值依赖的目的.理论分析和仿真结果表明,改进的OMP算法比原有算法有更理想的重构效果,有更高的重构精度.     

通过正交匹配追踪研究压缩感知信号检测算法

现阶段,我国应用的检测算法大多以特征量的迭代过程为研究对象,这种检测方法只适用于感知信号存在时,并不适用于全部的信号测算工作。本文将提出感知信号检测的改进方法和正交匹配追踪的研究方案,以降低信号特征量的变化区间,提高感知信号检测结果的准确性,提高检测的成功率。     

分布式压缩感知实现联合信道估计的方法

针对无线通信中多个信道之间存在相关性的现象,本文研究了基于压缩感知的联合信道估计。通过选取多个节点与簇头之间的信道为研究背景,本文建立了多信道下的联合信道估计模型,推导了判决门限与信噪比之间的关系,提出了基于门限自适应-正交匹配追踪联合重构技术(TA-SOMP)的信道估计算法,并进行了相应的仿真实验。仿真结果表明:与经典的正交匹配追踪(OMP)算法相比,本文算法所重构的信道与原始信道之间的均方误差(MSE)更小,传输信号误比特率(BER)更低;在相同信噪比环境下,TA-SOMP算法所需导频数量更少,频带利用率更高。      

压缩感知中基于变尺度法的贪婪重构算法的研究

首先将最优化方法中的梯度法与贪婪算法相结合,在已有梯度追踪算法的基础上提出了基于变尺度法的梯度追踪（VMMGP）算法,分析比较这些算法的计算复杂度和存储需求;其次用这些算法分别重构一维、二维信号,分析比较了算法重构效果及其性能好坏。实验结果表明,对于一维信号和二维信号的重构,所提出的VMMGP算法,重构效果是所有梯度追踪算法中最好的。     

Probabilistic greedy pursuit for streaming compressed spectrum sensing

This paper presents a probabilistic greedy pursuit(PGP)algorithm for compressed wide-band spectrum sensing under cognitive radio(CR)scenario.PGP relies on streaming compressed sensing(CS)framework,which differs from traditional CS processing way that only focuses on fixed-length signal’s compressive sampling and reconstruction.It utilizes analog-to-information converter(AIC)to perform sub-Nyquist rate signal acquisition at the radio front-end(RF)of CR,the measurement process of which is carefully designed for streaming framework.Since the sparsity of wide-band spectrum is unavailable in practical situation,PGP introduces the probabilistic scheme by dynamically updating support confidence coefficient and utilizes greedy pursuit to perform streaming spectrum estimation,which gains sensing performance promotion progressively.The proposed algorithm enables robust spectrum estimation without the priori sparsity knowledge,and keeps low computational complexity simultaneously,which is more suitable for practical on-line applications.Various simulations and comparisons validate the effectiveness of our approach.     

Asymptotics of greedy algorithms for variable-to-fixed lengthcoding of Markov sources

In this paper, alphabet extension for Markov sources is studied such that each extension tree is grown by splitting the node with the maximum value for a weight as a generalization of the leaf probability in Tunstall's (1967) algorithm. We show that the optimal asymptotic rate of convergence of the per-symbol code length to the entropy does not depend on an a priori selected proportional allocation of the sizes of the extension trees at the states. We show this without imposing restrictive conditions on the weight by which the trees are extended. Further, we prove the asymptotic optimality of an algorithm that allocates an increasing total number of leaves among the states. Finally, we give exact formulas for all the relevant quantities of the trees grown     

Adaptive algorithms to mitigate inefficiency in greedy geographical routing

This letter presents theoretical basis and practical algorithms for mitigating inefficiency in greedy geographical routing, which has great application potential in large scale ad hoc networks, such as sensor nets. Simulation results demonstrate the proposed algorithms' effectiveness and the capability to provide different efficiency-overhead tradeoffs.     

Automated reassembly of file fragmented images using greedy algorithms.

The problem of restoring deleted files from a scattered set of fragments arises often in digital forensics. File fragmentation is a regular occurrence in hard disks, memory cards, and other storage media. As a result, a forensic analyst examining a disk may encounter many fragments of deleted digital files, but is unable to determine the proper sequence of fragments to rebuild the files. In this paper, we investigate the specific case where digital images are heavily fragmented and there is no file table information by which a forensic analyst can ascertain the correct fragment order to reconstruct each image. The image reassembly problem is formulated as a k-vertex disjoint graph problem and reassembly is then done by finding an optimal ordering of fragments. We provide techniques for comparing fragments and describe several algorithms for image reconstruction based on greedy heuristics. Finally, we provide experimental results showing that images can be reconstructed with high accuracy even when there are thousands of fragments and multiple images involved.     

New bit loading algorithms for DMT systems based on the greedy approach

The performance of a DMT system, which transmits information over channels with varying characteristics through the frequency zones, is improved when the subchannels of the system are loaded with variable data rate. In this study, we meet the bit loading problem of the subcarriers of a DMT system. We propose two new optimum‐loading algorithms with low computational complexity. These algorithms assign integer number of bits successively until a target bit rate is fulfilled. We compare them with several existing algorithms in terms of transmitting energy versus data rate and complexity versus system's characteristics i.e. number of subcarriers and target data rate. Simulations prove that without sacrificing optimality both our proposals present a lower complexity level. Copyright © 2006 John Wiley & Sons, Ltd.     

Error concealment algorithms for robust decoding of MPEG compressed video

This paper provides some research results on the topic of error resilience for robust decoding of MPEG (Moving Picture Experts Group) compressed video. It introduces and characterizes the performance of a general class of error concealment algorithms. Such receiver-based error concealment techniques are essential for many practical video transmission scenarios such as terrestrial HDTV broadcasting, packet network based teleconferencing/multimedia, and digital SDTV/HDTV delivery via ATM (asynchronous transfer mode). Error concealment is intended to ameliorate the impact of channel impairments (i.e., bit-errors in noisy channels, or cell-loss in ATM networks) by utilizing available picture redundancy to provide a subjectively acceptable rendition of affected picture regions. The concealment process must be supported by an appropriate transport format which helps to identify image pixel regions which correspond to lost or damaged data. Once the image regions (i.e., macroblocks, slices, etc.) to be concealed are identified, a combination of spatial and temporal replacement techniques may be applied to fill in lost picture elements. A specific class of spatio-temporal error concealment algorithms for MPEG video is described and alternative realizations are compared via detailed end-to-end simulations for both one- or two-tier transmission media. Several algorithm enhancements based on directional interpolation, ‘I-picture motion vectors’, and use of MPEG-2 ‘scalability’ features are also presented. In each case, achievable performance improvements are estimated via simulation. Overall, these results demonstrate that the proposed class of error concealment algorithms provides significant robustness for MPEG video delivery in the presence of channel impairments, permitting useful operation at ATM cell-loss rates in the region of 10⁻⁴ to 10⁻³ and 10⁻² to 10⁻¹ for one- and two-tier transmission scenarios, respectively.     

基于压缩感知的偏振光成像技术研究

偏振成像技术是一种基于目标自身辐射或反射信号中所包含的偏振信息获取物体图像的方法,尤其在人工目标的探测和表面识别方面,相对光强度探测方式具有独特的优势。针对传统的偏振成像技术在复杂的成像环境中成像距离短和成像质量差的缺点,提出了一种基于压缩感知的新型偏振光成像技术。阐述了压缩感知理论的基本原理,构造了合适的采样矩阵和重构算法,设计了具体的成像系统,并通过压缩感知偏振成像实验证明了该成像技术的可行性。空气中实验结果表明,该成像系统能够重构出预先放置目标靶的偏振图像。此外在现有的实验条件基础上讨论并提出了几种改进系统成像质量的措施。     

压缩域运动补偿中的快速算法研究

研究了压缩域运动补偿的快速算法，着重从数学表达方式上研究了当进行宏块预测时，充分利用参考帧中公共块的计算方法，与DCT矩阵分解的快速算法相比，在不影响图像质量的同时。其计算效率提高了26．5％。     

压缩感知理论在语音信号去噪中的应用

针对小波阈值滤波的局限性,将压缩感知理论应用到语音信号去噪中,并与小波阈值滤波方法进行了比较,仿真实验结果表明：基于压缩感知的小波滤波方法可以有效地去除语音信号中的噪声,并且去噪效果优于传统小波阈值滤波方法,对工程中音频信号的降噪具有指导意义。