一种利用压缩感知改进的PMF-FFT扩频捕获算法

为了实现直接序列扩频（DSSS）信号快速捕获的同时降低数据量和硬件资源消耗,引入了压缩感知理论改进部分匹配滤波-快速傅里叶变换（PMF-FFT）算法,提出了基于压缩感知改进的部分匹配滤波-快速傅里叶变换（CSPMF-FFT）算法。该算法将PMF-FFT算法与压缩感知理论相结合,先对信号进行稀疏性分析和压缩观测,然后从少量压缩观测值中重构信号,并利用输出的峰值信息估算信号的多普勒频移和码相位,从而实现捕获。理论分析和仿真实验表明,相较于PMF-FFT捕获算法,CSPMF-FFT算法能在成功完成捕获的同时有效地减少相关器的数目和FFT变换的运算量,从而降低系统数据量和硬件资源压力,为基于压缩感知的扩频信号处理技术研究奠定了基础。     

基于差分变换的语音信号压缩感知

信号在某种变换下可以稀疏表示是压缩感知研究的先验条件,正交傅里叶变换则是应用非常广泛的一种稀疏变换。但是,由于语音信号是准周期信号,对其进行傅里叶变换会造成频谱泄漏,因而引起信号重构性能的降低。本文基于语音信号准周期性的特点,提出了一种基于差分变换的语音稀疏化变换矩阵,在此基础上采用OMP优化算法来重构语音信号。实验表明,与采用正交傅里叶变换方法对语音信号进行稀疏化变换、OMP算法对语音信号进行重构的方法相比,差分变换方法的性能明显优于正交傅里叶变换的方法,即在相同重构性能时,差分变换的压缩比小于正交傅里叶变换,因而差分变换的方法大大提高了信号的压缩性能。PESQ对重构语音质量评测的结果表明差分变换方法重构的语音信号MOS得分较高,这也说明对于语音信号这一特殊信号,差分变换法具有很大的优越性。      

时分MIMO滑坡雷达稀疏成像算法

针对现用于成像的MIMO山体滑坡雷达均匀线性阵列数目过多、数据处理复杂度高的问题，引入稀疏阵列时分地基MIMO雷达模型，提出一种基于逆傅里叶变换和混合匹配追踪算法的成像方法。首先通过对雷达回波信号作逆傅里叶变换实现距离向压缩，并进行近似相位补偿，然后采用一种基于时延补偿因子稀疏基的压缩感知算法实现方位向压缩。同时针对多目标成像的伪影点问题，方位向数据压缩引入子空间追踪算法和正交匹配追踪算法的结合算法重构出高分辨率且没有伪影的二维图像。根据真实的山体滑坡监测成像场景参数，通过数值仿真验证了该方法能够在低于传统均匀阵列的天线数目情况下实现目标高质量成像，且具有一定的抗噪性。     

匹配傅里叶变换快速算法及在雷达信号处理中应用

为了减小匹配傅里叶变换分析的计算量,提出了一种基于快速傅里叶变换的快速算法。根据匹配傅里叶变换的分解将积分形式转化为离散形式,推导出快速算法表达式。该算法与直接的数值离散匹配傅里叶变换算法相比较,计算量大大减少。同时给出了其在雷达信号处理中线性调频信号的检测与参数估计的应用。理论及计算机仿真结果表明了该算法的有效性和精确性,有良好的工程应用前景。     

应用于电能质量的压缩感知稀疏基的研究

为了解决基于傅里叶变换基的压缩感知对电能质量干扰信号压缩采样丢失时变信息的问题,本文进行了基于小波变换基的压缩感知电能质量研究。首次提出采用不同小波基的小波变换基作为稀疏基,来提高压缩感知对电能质量干扰信号的重构效果,为电能质量研究提供了一种新的研究方向;并通过实验仿真对比了基于傅里叶变换基和基于小波变换基的压缩感知重构效果。在压缩感知重构算法分别采用正交匹配追踪算法和压缩采样匹配追踪算法下,仿真结果表明,压缩感知应用于电能质量时,基于小波变换基的压缩感知重构效果优于基于傅里叶变换基的压缩感知重构效果;当压缩采样比是20％,稀疏基采用db3小波变换基时,均方误差均低于0．1％,良好地完成了原始电能质量干扰信号的重构。     

基于压缩感知的伪随机等效采样信号重构

伪随机等效采样利用采样周期数与采样点数间的互质关系使各采样点均匀复现于同一周期,从而达到较高的等效采样速率。然而为了精确重构出原始信号,需大量采样数据,因此导致采样时间过长,实时性能差。针对上述问题,提出了一种基于压缩感知理论的伪随机等效采样信号重构方法,通过构造伪随机等效采样观测矩阵并选择离散傅里叶变换基建立稀疏重构模型,然后利用压缩感知中的正交匹配追踪算法求解该模型,从而重构出原始信号。仿真实验表明,所提方法在采样点个数40时,重构成功率达99.73%。     

基于随机滤波的探地雷达成像方法

探地雷达是一种超宽带雷达系统,若按传统的奈奎斯特采样,雷达回波信号需要大量空间存储。压缩感知可以实现利用少量的测量值对稀疏信号进行重构,其中最为关键的是测量矩阵和重构算法的选择。本文将压缩感知应用于探地雷达成像,并利用随机滤波的思想选择测量矩阵,可以有效减少测量矩阵中非零值的个数。利用正交匹配追踪算法对信号进行重构,算法简单,降低了数据的存储量和运算复杂度,该算法同样可以对时间和空间上同时压缩的数据进行成像。最后,本文给出基于时间连续信号的GPR接收机一种CS实现方案。仿真结果表明,本文提出的成像方法可以以少量数据精确地对信号进行重构,并且运算量少。      

语音重构的DCT域加速Landweber迭代硬阈值算法

重构信号的最基本理论依据是该信号在某个变换域是稀疏的或近似稀疏的。基于语音信号在DCT域的近似稀疏性,可以采用压缩感知(Compressed Sensing, CS)理论对其进行重构。压缩感知理论中的迭代硬阈值(Iterative hard thresholding, IHT)算法以其较好的性能被广泛用来重构信号,但其收敛速度比较慢,如何提高收敛速度,一直是迭代硬阈值算法研究的重点之一。针对压缩感知理论中的IHT算法收敛速度相当慢的问题,提出了语音重构的DCT域加速Landweber迭代硬阈值(Accelerated Landweber iterative hard thresholding, ALIHT)算法。该算法对原始语音信号做DCT变换,然后在DCT域将每一步Landweber迭代分解为矩阵计算和求解两步,通过修改其中的矩阵计算部分实现Landweber迭代加速,最后通过迭代硬阈值对信号做阈值处理。实验结果表明,加速Landweber迭代硬阈值算法加快了收敛速度、减少了计算量。      

两级分辨率稀疏重构线性调频信号参数估计

为解决压缩感知(Compressed Sensing,CS)算法在线性调频(Linear Frequency Modulation,LFM)信号参数估计中计算量较大的问题,提出了两级分辨率稀疏重构参数估计算法。该算法在离散线性调频傅里叶变换的基础上,采用低分辨率观测矩阵,获取信号调频率和中心频率的先验信息,根据先验信息构造有约束的高分辨率观测矩阵,精确估计出调频率和中心频率两个参数,实现LFM信号的重构,达到了减小计算量的目的。仿真实验表明,该算法能够准确估计单个和多个LFM信号的参数,并且算法的参数估计性能明显优于传统算法。     

一种基于多维交替方向乘子法的多输入多输出逆合成孔径雷达成像方法

基于傅里叶变换的传统逆合成孔径雷达(ISAR)成像方法存在数据存储量大、数据采集时间长的问题。压缩感知(CS)理论利用图像的稀疏性,可以利用有限的数据恢复图像,这极大降低了数据采集成本。但对于多维数据,传统压缩感知方法要将多维数据转化成一维向量,这造成了很大存储和计算负担。因此,该文提出一种基于多维度-交替方向乘子法(MD-ADMM)的多输入多输出-逆合成孔径雷达(MIMO-ISAR)成像快速稀疏重建方法。首先建立基于张量信号的压缩感知模型,然后用ADMM算法对模型进行优化,将测量矩阵分解为张量模态积,用张量元素除法替代矩阵求逆,显著减少所需的内存和计算负担。该方法只需少量的数据采样,就能实现快速成像。与其他基于张量的压缩感知方法相比,该方法具有鲁棒性强、图像质量好、计算效率高的优点。仿真和实测数据验证了该方法的有效性。      

A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise

The letter presents a new algorithm for the precise estimation of the frequency of a complex exponential signal in additive, complex, white Gaussian noise. The discrete Fourier transform (DFT)-based algorithm performs a frequency interpolation on the results of an N point complex fast Fourier transform. For large N and large signal to noise ratio, the frequency estimation error variance obtained is 0.063 dB above the Cramer-Rao bound. The algorithm has low computational complexity and is well suited for real time digital signal processing applications, including communications, radar and sonar.     

Distribution agnostic Bayesian compressive sensing with incremental support estimation

In most compressive sensing algorithms, such as L1-optimization and greedy family techniques, the only a priori information utilized in the reconstruction procedure is the sparsity information. Meanwhile, there exists another family of techniques based on the Bayesian strategy, which considers comprehensive a priori statistical knowledge of the sparse data. This feature resulted in more increased attention to this category of algorithms. One member of the Bayesian-based family of compressive sensing reconstruction algorithms is the support Agnostic Bayesian Matching Pursuit, which is agnostic to support distribution.However, its high computation complexity in determining the set of dominant supports makes this algorithm unfeasible for practical applications such as wireless sensor networks (WSNs). Due to the special conditions of WSNs, consists of limited-power sensors, developed algorithms for them must have the least possible amount of computations. Given this, in this paper, we propose a Bayesian-based method with incremental support detection for distributed sparse signal recovery, which considerably reduces computational complexity. In the proposed method, in a network of sensors, sparse signal reconstruction from noisy measurements is done distributively and in the form of incremental cooperation. So, the number of required computations will be significantly reduced, which will result in a fast approach. The computer simulations show the superior performance of the proposed incremental Bayesian recovery method.

     

Fast detection and parameter estimation for polyphase-code radar signal

The detection and parameter estimation for polyphase-code radar signal are analysed in this article. In view of the fact that traditional algorithms of signal detection and parameter estimation have enormous computational complexity, a joint fast algorithm employed fractional operation is proposed to detect the polyphase-code radar signal and estimate its modulation parameter. The proposed algorithm firstly detects the signal and estimates the sweep rate with the detection statistics derived from fractional autocorrelation. Then proposed algorithm achieves the estimation of other modulation parameters by using fractional Fourier transform (FrFT). Simulation results have verified the effectiveness of the proposed algorithm. Compared with traditional algorithms, proposed algorithm has identical performance of detection and parameter estimation, but can remarkably reduce computational cost. The proposed algorithm is suitable for the application of practical equipment.     

基于OMP的非合作宽带脉冲压缩雷达信号的压缩感知研究

压缩感知技术可以用来实现对非合作宽带信号的欠采样快速处理。宽带脉冲压缩雷达能够有效解决雷达探测距离和距离分辨力的矛盾,在探测领域得到了广泛应用,为实现对非合作宽带脉冲压缩雷达信号的快速欠采样接收处理,本文首先开展了信号稀疏分解与重构算法研究,通过对贪婪算法、凸松弛类算法、组合类算法三大算法进行对比分析,选用了运行速度快且重构精度高的正交匹配追踪(OMP)算法针对非合作宽带脉冲压缩雷达信号进行压缩感知仿真分析。仿真结果表明:在一定信噪比条件下,OMP算法完全能够实现对非合作宽带脉冲压缩雷达信号的欠采样和信号重构,从而实现了对非合作宽带雷达信号的欠采样处理,为处理非合作超宽带雷达信号提供了很好的理论指导。     

A multilevel matrix decomposition algorithm for analyzingscattering from large structures

A multilevel algorithm is presented for analyzing scattering from electrically large surfaces. The algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics. The algorithm permits a fast matrix-vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks, with each describing the interaction between distant scatterers. The multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast Fourier transform (FFT) and that only relies on well-known algebraic techniques. The computational complexity and the memory requirements of the proposed algorithm are O(N log² N)     

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.

     

DIFFT: A Fast and Accurate Algorithm for Fourier Transform Integrals of Discontinuous Functions

A new highly accurate fast algorithm is proposed for computing the Fourier transform integrals of discontinuous functions (DIFFT) by employing the analytical Fourier transforms of Gauss–Chebyshev–Lobatto interpolation polynomials and the scaled fast Fourier transform. This algorithm can achieve the exponential accuracy for evaluation of Fourier spectra at the whole frequency range with a low computational complexity. Furthermore, the algorithm allows the adaptive sampling densities for different sections of a piecewise smooth function. Numerical experiments are shown for the applications in computational electromagnetics.      

实值离散Gabor变换块时间递归算法的并行格型结构实现方法

Gabor变换在很多领域被认为是非常有用的方法,如语音与图像处理,雷达、声纳、振动信号的处理与理解等,然而实时应用却因其很高的计算复杂性而受到限制.为了减小计算复杂性,我们曾提出了实值离散Gabor变换法.本文首先简单回顾了作者曾提出的实值离散Gabor变换及其与复值离散Gabor变换的关系,然后为了有效地和快速地计算实值离散Gabor变换,提出了在临界抽样条件下和在过抽样条件下,一维实值离散Gabor变换系数求解的块时间递归算法以及由变换系数重建原信号的块时间递归算法,研究了两算法使用并行格型结构的实现方法,并讨论和比较了算法的计算复杂性和优越性.