基于双阈值的压缩采样匹配追踪改进算法

针对基于压缩感知的压缩采样匹配追踪(CoSaMP)算法迭代次数严重依赖于信号稀疏度,候选原子冗余度大,从而导致最终的支撑原子集选择时间长、选择精度低等问题,提出一种基于双阈值的压缩采样匹配追踪算法.该算法利用模糊阈值进行支撑集候选原子的选择,引入残差与观测矩阵的相关度变化阈值作为迭代停止条件,对图像进行重构.仿真实验表明,所提出的算法重构速度快,重构效果优于CoSaMP算法.     

压缩感知中迂回式匹配追踪算法

迂回式匹配追踪(detouring matching pursuit,DMP)是一种计算复杂度低、准确率高、对传感矩阵列相关性要求低的贪婪重构稀疏信号算法.DMP中子内积逆和系数矩阵递增递减核心式被提出并证明,DMP利用子内积逆和系数矩阵减少残差误差变化量的计算量,达到降低计算复杂度的目的.另外,DMP采用先逐个最优缩减、后逐个最优扩增假定支撑集元素的方法提高重构准确率和扩大重构稀疏信号的稀疏度范围.DMP算法复杂度分析表明,DMP算法中获取、缩减和扩增假定支撑集的复杂度分别为O(K2 N),O(b(K-b)N)和O(b(K-b)N).加权间接重构0-1稀疏信号实验结果表明,对于稀疏度为M/2的0-1稀疏信号,DMP、逐步贪婪追踪(greedy pursuit algorithm,GPA)、子空间追踪(subspace pursuit,SP)、压缩采样追踪(compressive sampling matching pursuit,CoSaMP)、正交匹配追踪(orthogonal matching pursuit,OMP)的重构准确率分别为99%,65%,0%,0%和13%.非零值服从正态分布的稀疏信号实验结果也表明DMP的重构准确率优势显著.     

改进的压缩采样匹配追踪算法

针对压缩采样匹配追踪( CoSaMP)算法重构精度相对较差的问题,为了提高算法的重构性能,提出了一种基于伪逆处理改进的压缩采样匹配追踪( MCoSaMP)算法。首先,在迭代前,对观测矩阵进行伪逆处理,以此来降低原子间的相干性,从而提高原子选择的准确性;然后,结合正交匹配追踪算法( OMP),将OMP算法迭代K次后的原子和残差作为CoSaMP算法的输入;最后,每次迭代后,通过判断残差是否小于预设阈值来决定算法是否终止。实验结果表明,无论是对一维高斯随机信号还是二维图像信号,MCoSaMP算法的重构效果优于CoSaMP算法,能够在观测值相对较少的情况下,实现信号的精确重构。     

一种改进的压缩采样匹配追踪算法研究

该文简单对信号稀疏重建的模型和测量矩阵的设计进行了介绍,主要介绍了几种稀疏重建算法,详细给出压缩采样匹配追踪算法及其改进算法的数学框架和基本思想,从原子选择策略和冗余向量的更新方式对算法进行了比较分析,最后通过模拟实验验证了MP,OMP,CoSaMP和IHTCoSaMP算法的重构效果,同时以MSE为性能指标评价了各种算法的重构质量,实验结果表明改进的压缩抽样匹配追踪算法的运算速度较快,重构质量较高。     

一种改进的压缩感知重构算法

压缩感知重构信号时,在感知过程中如何选定支撑集对算法的重构性能至关重要.基于压缩采样匹配(CoSaMP)重构算法,引入Dice系数匹配性度量准则,优化了支撑集的选择.上述算法改进了从给定的观测矩阵中挑选与残差信号最匹配原子的匹配准则,体现了残差信号中各个元素对原子选取的重要作用.仿真结果表明:在同等稀疏的条件下,重构算法与传统的CoSaMP算法相比,误差低于传统CoSaMP算法,且随着观测维数的增加,重构信号的平均成功概率比传统的CoSaMP算法的大,实现了较小的重构误差和更好的压缩性能.     

分段迭代匹配追踪图像重构算法

目的 压缩采样匹配追踪（CoSaMP）算法虽然引入回溯的思想,但其原子选择需要大量的观测值且在稀疏度估计不准确时,会降低信号重构精度,增加重构时间,降低重构效率。为提高CoSaMP算法的重构精度,改善算法的重构性能,提出了一种基于广义逆的分段迭代匹配追踪（StIMP）算法。方法 为保证迭代时挑选原子的精确性和快速性,对观测矩阵广义逆化,降低原子库中原子的相干性;原子更新结合正交匹配追踪（OMP）算法筛选原子的准确性与CoSaMP算法的回溯性,将迭代过程分为两个阶段：第1阶段利用OMP算法迭代K/2次;第2阶段以第1阶段OMP算法迭代所得的残差和原子为输入,并采用CoSaMP算法继续迭代,同时改变原子选择标准,从而精确快速地重构出稀疏信号。结果 对于1维的高斯随机信号,无论在不同的稀疏度还是观测值下,相比于OMP、CoSaMP、正则化正交匹配追踪（ROMP）算法和傅里叶类圆环压缩采样匹配追踪（FR-CoSaMP）算法,StIMP算法更加稳健,且具有更高重构成功率;对于2维图像信号,在各个采样率下,StIMP算法的峰值信噪比（PSNR）均高于其他重构算法,在采样率为0.7时,StIMP算法的平均PSNR值比OMP、CoSaMP、ROMP和FR-CoSaMP算法分别高2.14 dB、1.20 dB、3.67 dB和0.90 dB,平均重构时间也较OMP、CoSaMP和FR-CoSaMP算法短。结论 提出了一种改进的重构算法,对1维高斯随机信号和2维图像信号均有更好的重构效率和重构效果,与原算法和现有的主流图像重构方法相比,StIMP算法更具高效性和实用性。     

基于小波树模型的CoSaMP压缩感知算法

无线传感网络存在网络带宽限制和传感器节点的能耗问题,实际应用中通常希望可以通过重构算法从采集的少量数据中还原出原始信息,压缩感知理论为上述问题提供了一个解决思路。利用压缩感知理论,对无线传感器网络中温度传感器的监测信号进行了压缩感知的应用研究。针对传统压缩采样匹配追踪(CoSaMP)算法中测量次数多、重构精度低等问题,利用信号的小波系数所形成的连通树的结构特性,提出了基于小波树模型的压缩采样匹配追踪算法。将该算法应用到无线传感器网络监测信号的压缩感知仿真实验中,与传统压缩采样匹配追踪算法的重构性能进行比较,结果表明该算法较传统压缩采样匹配追踪算法在一定范围内对无线传感器网络中的温度信号具有更好的压缩感知性能。     

基于压缩感知CoSaMP算法的精确重构

为有效解决压缩采样匹配追踪(Compressive Sampling Matching Pursuit, CoSaMP)算法对稀疏度K值的依赖问题,提高重构精度,提出了一种根据峰值信噪比增减变化趋势来确定最佳迭代次数的CoSaMP改进算法。先将PSNR算式进行数学推导演变,将算式中未知的原始信号巧妙转换为已知信号,并证明了此转换式与PSNR算式有相同增减性,在迭代过程中基于此转换式可根据各列稀疏度的不同,自适应的确定不同列的最佳迭代次数,从而保证更高的重构精度。理论分析和实验仿真表明,改进的CoSaMP算法比原有算法有更理想的重构效果,与其它重构算法相比有更高的重构成功率,并且更具高效性和实用性。     

基于压缩感知信号重建的自适应正交多匹配追踪算法*

近年来出现的压缩感知理论为信号处理的发展开辟了一条新的道路,不同于传统的奈奎斯特采样定理,它指出只要信号具有稀疏性或可压缩性,就可以通过少量随机采样点来恢复原始信号。在研究和总结传统匹配算法的基础上,提出了一种新的自适应正交多匹配追踪算法(adaptive orthogonal multi matching pursuit,AOMMP)用于稀疏信号的重建。该算法在选择原子匹配迭代时分两个阶段,引入自适应和多匹配的原则,加快了原子的匹配速度,提高了匹配的准确性,实现了原始信号的精确重建。最后与传统OMP算法     

基于压缩感知的稀疏度自适应匹配追踪改进算法

针对稀疏度自适应匹配追踪(Sparsity adaptive matching pursuit,SAMP)算法存在预选原子过多、重构时间长、步长的选择固定等缺点,提出一种稀疏度自适应匹配追踪改进算法.该算法将稀疏度预先设定值与稀疏度估计过量判据相结合进行真实稀疏度快速估计,通过模糊阈值的方法提高候选原子的精确度,采用原子相关阈值改善迭代停止条件,最终实现信号的精确重构.仿真实验表明,改进算法重构质量较好于SAMP算法,重构速率显著提高.     

用于图像重构的基于行间支撑集相似度的CoSaMP算法

压缩采样匹配追踪(CoSaMP)算法的性能受初始支撑集选择的制约,初始支撑集选择不准确不仅影响重构精度,还会降低重构速度。针对该问题,将图像在稀疏域的结构特性引入到CoSaMP算法中,提出了支撑集相似度的概念;利用数字图像相邻行之间原子支撑集的相似性,提出了基于行间支撑集相似度的CoSaMP算法。实验结果表明,在同等采样率的条件下, 与传统的CoSaMP算法相比,所提算法在不增加算法时间复杂度的同时提高了重构质量 ,峰值信噪比提高了0.6~2.5dB。     

Rapid real-time generation of super-resolution hyperspectral images through compressive sensing and GPU

Recently, compressive sensing (CS) has offered a new framework whereby a signal can be recovered from a small number of noisy non-adaptive samples. This is now an active area of research in many image-processing applications, especially super-resolution. CS algorithms are widely known to be computationally expensive. This paper studies a real time super-resolution reconstruction method based on the compressive sampling matching pursuit (CoSaMP) algorithm for hyperspectral images. CoSaMP is an iterative compressive sensing method based on the orthogonal matching pursuit (OMP). Multi-spectral images record enormous volumes of data that are required in practical modern remote-sensing applications. A proposed implementation based on the graphical processing unit (GPU) has been developed for CoSaMP using computed unified device architecture (CUDA) and the cuBLAS library. The CoSaMP algorithm is divided into interdependent parts with respect to complexity and potential for parallelization. The proposed implementation is evaluated in terms of reconstruction error for different state-of-the-art super-resolution methods. Various experiments were conducted using real hyperspectral images collected by Earth Observing-1 (EO-1), and experimental results demonstrate the speeding up of the proposed GPU implementation and compare it to the sequential CPU implementation and state-of-the-art techniques. The speeding up of the GPU-based implementation is up to approximately 70 times faster than the corresponding optimized CPU.     

基于改进CoSaMP算法的图像重建

重构算法是压缩感知的核心技术之一,直接决定着压缩感知能否可以在实际系统中进行应用。为提高压缩感知的重构精度同时缩短处理时间,本文引进加权与矩阵分块技术,与压缩采样匹配追踪(Compressive Sampling Matching Pursuit, CoSaMP)算法相结合,使原始算法更加完善。仿真结果表明,当稀疏条件同等的情况下进行重构,改进的算法与原始算法相比重构质量有所提高。     

Parallel compressive sampling matching pursuit algorithm for compressed sensing signal reconstruction with OpenCL

Compressive sensing (CS) is a new signal processing method, which was developed recent years. CS can sample signals with a frequency far below the Nyquist frequency. CS can also compress the signals while sampling, which can reduce the usage of resources for signal transmission and storage. However, the reconstruction algorithm used in the corresponding decoder is highly complex and computationally expensive. Thus, in some specific applications, e.g., remote sensing image processing for disaster monitoring, the CS algorithm usually cannot satisfy the time requirements on traditional computing platforms. Various studies have shown that many-core computing platforms such as OpenCL are among the most promising platforms that are available for real-time processing because of their powerful floating-point computing capabilities. In this study, we present the design and implementation of parallel compressive sampling matching pursuit (CoSaMP), which is an OpenCL-based parallel CS reconstruction algorithm, as well as some optimization strategies, such as access efficiency, numerical merge, and instruction optimization. Based on experiments using remote sensing images with different sizes, we demonstrated that the proposed parallel algorithm can achieve speedups of about 41 times and 58 times on AMD HD7350 and NVIDIA K20Xm platforms, respectively, without modifying the application code.     

基于位置集回验的并联分片频谱压缩感知算法

提出了基于压缩感知的认知无线电频谱检测方法,该方法采用并联分片压缩采样法,同时引入了基于位置集回验的重构算法.分析了不同重构算法的性能差异,阐述了并联分片压缩采样的实现方法.通过仿真分析了不同分片数条件下,并联分支数对CoSaMP和OMP重构算法重构概率的影响,并说明了频带划分的估计方法.     

基于压缩感知信号重建的自适应空间正交匹配追踪算法

传统的奈奎斯特采样定理规定采样频率最少是原信号频率的两倍,才能保证不失真的重构原始信号,而压缩感知理论指出只要信号具有稀疏性或可压缩性,就可以通过采集少量信号来精确重建原始信号.在研究和总结已有匹配算法的基础上,提出了一种新的自适应空间正交匹配追踪算法(Adaptive Space Orthogonal Matching Pursuit,ASOMP)用于稀疏信号的重建.该算法在选择原子匹配时采用逆向思路,引入正则化自适应和空间匹配的原则,加快了原子的匹配速度,提高了匹配的准确性,最终实现了原始信号的精确重建.最后与传统MP和OMP算法进行了仿真对比,结果表明该算法的重建质量和算法速度均优于传统MP和OMP算法.     

A Bayesian approach to SAR imaging

We introduce a new approach using the Bayesian framework for the reconstruction of sparse Synthetic Aperture Radar (SAR) images. The algorithm, named SLIM, can be thought of as a sparse signal recovery algorithm with excellent sidelobe suppression and high resolution properties. For a given sparsity promoting prior, SLIM cyclically minimizes a regularized least square cost function. We show how SLIM can be used for SAR image reconstruction as well as SAR image enhancement. We evaluate the performance of SLIM by using realistically simulated complex-valued backscattered data from a backhoe vehicle. The numerical results show that SLIM can satisfactorily suppress the sidelobes and yield higher resolution than the conventional matched filter or delay-and-sum (DAS) approach. SLIM outperforms the widely used compressive sampling matching pursuit (CoSaMP) algorithm, which requires the delicate choice of user parameters. Compared with the recently developed iterative adaptive approach (IAA), which iteratively solves a weighted least squares problem, SLIM is much faster. Due to the computational complexity involved with SAR imaging, we show how SLIM can be made even more computationally efficient by utilizing the fast Fourier transform (FFT) and conjugate gradient (CG) method to carry out its computations. Furthermore, since SLIM is derived under the Bayesian model, the a posteriori distribution given by the algorithm provides us with a confident measure regarding the statistical properties of the SAR image pixels.