基于压缩感知的探地雷达成像算法研究

压缩感知理论通过从一系列非自适应线性测量中求解一个凸L_1最小化问题,从而对稀疏信号进行重构。该文基于压缩感知理论对宽带合成孔径雷达成像,利用空间目标信号成像的稀疏性,提出了一种全新的低采样率数据采集重构算法。此算法在获取雷达信号原始数据时采用压缩感知的算法,减少了原始信号数据的采样量,并且用少量的测量数据和测量孔径获得重建测量目标的信息。最后将此算法与传统的反投影成像进行了比较,其仿真试验数据表明,基于压缩感知的探地雷达成像算法比传统反向投影算法成像效果好,且所需数据量少。     

压缩感知理论与非凸优化方法研究

针对某些信号带宽较宽导致难以直接采样的问题,压缩感知理论提供了一种可行的低速采样方法。信号在特定变换域中拥有稀疏表示,通过低速采样得到少量的投影值,已经包含了重构所需的重要信息。利用压缩感知理论从投影值中重构出稀疏向量,进而重建原信号。同时介绍一种基于非凸优化的压缩感知重构算法。相比L1范数的凸优化和无稀疏约束的L2范数,非凸优化的Lp范数拥有对稀疏性更强的约束。实验结果表明,使用压缩感知理论可以显著降低对信号的采样速率,而使用非凸优化算法可以取得更好的重构效果。     

基于压缩感知的多发多收高分辨SAR成像算法研究

压缩感知理论指出,稀疏信号可以通过以低于奈奎斯特采样的测量数据重建出原始信号。针对高分辨率SAR成像在奈奎斯特理论下所面临的高速A／D采样、大数据量存储、传输等问题挑战。本文提出了一种基于压缩感知理论的多发多收高分辨率SAR二维成像算法。该算法减轻了高分辨率SAR成像的压力,采用压缩感知处理降低了A／D采样速率、数据量...     

CS与GPR联合反演目标成像

压缩传感(CS)理论是在已知信号具有稀疏性或可压缩性的条件下对信号数据进行采集、编解码的新理论。压缩传感采用非自适应线性投影来保持信号的原始结构,能通过数值最优化问题准确重构原始信号。压缩传感以远低于奈奎斯特频率进行采样,在高分辨压缩成像系统、视频图像采集系统、雷达成像以及MRI医疗成像等领域有着广阔的应用前景。阐述了压缩传感理论框架以及信号稀疏表示、CS编解码模型,并进行了压缩传感与探地雷达联合反演目标成像。反演结果表明,随机孔径压缩传感成像算法比递归反向投影算法和最小二乘法所需数据量少,成像效果好,目标旁瓣小,对噪声的鲁棒性更好。     

基于混合范数稀疏约束的ISAR高分辨成像算法

基于逆合成孔径雷达(ISAR)信号的稀疏性，提出了一种基于混合范数稀疏约束的ISAR高分辨成像算法。该方法通过利用压缩感知理论建立了一个基于l_2,0混合范数稀疏约束下的最优化ISAR信号模型，通过求解该最优化模型实现短相干积累时间下ISAR图像的高分辨重建。该模型利用了l_2,0混合范数的优势，运算时可实现更快收敛，大大提高了模型求解的运算速度；同时，该最优化模型在求解时采用了共轭梯度下降法和快速傅里叶变换操作，提高了算法的求解运算效率。仿真和实测数据都验证了方法的有效性。     

压缩感知理论及其应用前景

压缩感知理论是近年来提出的一种基于信号稀疏性的新兴采样理论。与通常的数据采样定理不同,该理论提出可以用远远少于传统采样定理所需的采样点数或观测点数恢复出原信号或图像。本文主要阐述了压缩感知中信号的稀疏表示、测量矩阵的设计及信号的重构算法等基本理论,论述了该理论的广阔应用前景。     

基于多层小波变换的压缩感知图像快速复原算法研究

为了能够有效地改善低码率压缩图像的主客观质量,减少图像复原所需观测数据量,节约存储空间和计算量,提出了一种基于多层小波变换的压缩感知图像快速复原算法。该算法将压缩感知理论中的信号重构方法运用于图像复原领域,建立基于压缩感知的图像复原模型,通过少量低维投影空间的测量值并根据信号稀疏表示的先验知识对信号进行精确或高概率的复原。通过Matlab进行实验仿真,结果表明,该算法与传统的图像复原算法相比,通过相同的观测数据量可以获得更高的PSNR,复原效率也得到了提高。     

采用正交多项匹配的块稀疏信号重构算法

压缩感知,通过测量矩阵将原始信号从高维空间投影到低维空间,然后求解优化问题,从少量投影中重构出原始信号,是一种有效的信号采集技术。块稀疏信号是具有特殊结构的稀疏信号,其非零值是成块出现的。针对该信号的特点,提出一种采用正交多项匹配的块稀疏信号重构算法。该算法每次迭代选择多个最大相关子块,然后更新块索引集,以及迭代余量,最后求广义逆运算重构出原始信号。仿真结果表明,相比于大多数的现有算法,本文算法重构概率较高,运行时间较短,复杂度较低。      

基于压缩感知的随机噪声成像雷达

近年来提出的压缩感知(CS)理论指出可以从很少的采样点中以很大的概率准确重建原始的未知稀疏信号。该文将压缩感知与随机噪声雷达相结合,提出了基于压缩感知的随机噪声雷达,并给出了该雷达系统的基本原理框图,从理论上证明了基于压缩感知的随机噪声雷达的回波观测矩阵具有很好的等容性质,在目标场景稀疏或可以稀疏表示时,基于压缩感知的随机噪声雷达可以采集远小于常规随机噪声雷达成像所需的回波数据并能实现准确成像,最后通过仿真实验验证了该文的结论。     

压缩感知中测量矩阵与重建算法的协同构造

本文提出基于感知字典的迭代硬阈值(SDIHT)算法,以此协同构造压缩感知中测量矩阵与重建算法.将成对测量矩阵与感知字典分别用于压缩投影和构造重建算法,重建迭代至残差为零,从而精确恢复原始稀疏信号.本文证明了SDIHT算法精确恢复原始稀疏信号的充分条件.SDIHT算法的优点是重建精度高和计算复杂度低.仿真实验表明,当信号稀疏度或测量次数相同时,相比IHT、OMP和BIHT算法,SDIHT算法重建0-1稀疏信号和二维图像效果更好、算法效率更高.     

基于面阵CCD-TDI模式编码感知的高分辨率遥感计算成像

针对推扫式遥感成像,基于压缩感知(CS)理论,提出一种利用低密度探测器获取高分辨率遥感图像的新方法。在推扫过程中,采用可编码的行间转移面阵电荷耦合器件(CCD)并使其工作于时间延迟积分(TDI)模式,在随机曝光控制电路的控制下实现对场景信息的编码感知;通过计算成像,从感知的数据中重构出高分辨率遥感图像。这种基于CCD-TDI模式编码感知的高分辨率遥感计算成像方法,可以增强成像分辨率和提高输出图像信噪比。仿真结果验证了本文方法的有效性。     

正交预处理在DSSS信号压缩感知中的应用

直接序列扩频信号因具有良好的隐蔽性和抗干扰性能被广泛应用,压缩感知能有效降低直扩信号的采样速率。当通过冗余字典稀疏分解直扩信号时,观测矩阵和稀疏基一般有强相关性,该文提出正交预处理(Orthogonal Pretreatment:OPT)方法对观测矩阵和稀疏基进行预处理,降低观测矩阵与稀疏基之间的相关性,从而提高信息恢复的精度与稳定性,仿真结果表明提出的方法有效。     

用于压缩感知的二值化测量矩阵

压缩感知是近年新兴的一种信号处理理论,在一定条件满足的情况下,压缩感知方法可通过远低于 Nyquist 频率的降采样数据以高概率近乎完美地重建原始信号。测量矩阵在压缩感知的整个处理过程中起着非常重 要的作用。本文从恢复算法入手提出二值化测量矩阵,并通过仿真对其性能加以验证。二值化后测量矩阵不仅在 性能上有一定提升,更重要的是可大大降低测量矩阵所需的存储空间以及压缩感知采样、恢复过程的运算量。     

An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.     

Restricted Structural Random Matrix for compressive sensing

Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. equal importance of CS measurements). However, there is a tradeoff. Improving sensing and compressing efficiency with prior signal information tends to favour particular measurements, thus decreasing security. This work aimed to improve the sensing and compressing efficiency without compromising security with a novel sampling matrix, named Restricted Structural Random Matrix (RSRM). RSRM unified the advantages of frame-based and block-based sensing together with the global smoothness prior (i.e. low-resolution signals are highly correlated). RSRM acquired compressive measurements with random projection of multiple randomly sub-sampled signals, which was restricted to low-resolution signals (equal in energy), thereby its observations are equally important. RSRM was proven to satisfy the Restricted Isometry Property and showed comparable reconstruction performance with recent state-of-the-art compressive sensing and deep learning-based methods.     

帧间自适应语音信号压缩感知

近年来提出的压缩感知是一种以低于传统奈奎斯特速率对信号采样可得到精确恢复的理论。该理论很快应用于简化传统的采样硬件、缩短采样时间、以及减少数据的存储空间。针对语音信号的传输问题,本文提出一种帧间自适应语音信号压缩感知的方法。在离散余弦变换域的语音信号具有稀疏性的前提下,以大量语音信号帧的分析统计为依据,提出一种基于语音帧能量分级和帧间位置惯性的语音信号自适应压缩感知算法。实验结果表明,能量自适应可以显著地提高语音信号的恢复质量,而位置自适应可以明显地减少语音信号的恢复时间,从而本文提出的算法可以用较少的恢复时间获得较好的恢复效果。      

Compressed sensing of complex-valued data

Compressed sensing (CS) is a recently proposed technique that allows the reconstruction of a signal sampled in violation of the traditional Nyquist criterion. It has immediate applications in reduction of acquisition time for measurements, simplification of hardware, reduction of memory space required for data storage, etc. CS has been applied usually by considering real-valued data. However, complex-valued data are very common in practice, such as terahertz (THz) imaging, synthetic aperture radar and sonar, holography, etc. In such cases CS is applied by decoupling real and imaginary parts or using amplitude constraints. Recently, it was shown in the literature that the quality of reconstruction for THz imaging can be improved by applying smoothness constraint on phase as well as amplitude. In this paper, we propose a general l_p minimization recovery algorithm for CS, which can deal with complex data and smooth the amplitude and phase of the data at the same time as well has the additional feature of using a separate sparsity promoting basis such as wavelets. Thus, objects can be better detected from limited noisy measurements, which are useful for surveillance systems.     

Compressed wide spectrum sensing scheme based on BP network

This paper proposes a compressed sensing (CS) scheme to reconstruct and estimate the signals. In this scheme, the framework of CS is used to break the Nyquist sampling limit, making it possible to reconstruct and estimate signals via fewer measurements than that is required traditionally. However, the reconstruction algorithms based on CS are normally non-deterministic polynomial hard (NP-hard) in mathematics, which makes difficulties in obtaining real-time analysis-results. Therefore, a new compressed sensing scheme based on back propagation (BP) neural network is proposed under an assumption that every sub-band is the same. In this new scheme, BP neural network is added into detection process, replacing for signal reconstruction and decision-making. By doing this, heavy calculation cost in reconstruction is moved into pre-training period, which can be done before the real-time analysis, bringing about a sharp reduction in time consuming. For simplify, 1-bit quantification is taken on compressed signals. Simulations demonstrate the performance enhancement in the proposed scheme: compared with normal CS-based scheme, the proposed one presents a much shorter response time as well as a better robustness performance to noise via fewer measurements.     

多分辨率压缩感知技术软件仿真与分析

压缩感知理论(Compressed Sensing,CS)为宽带信号的直接信息采样(Analog-to-Information,A-to-I)提供了解决方法。针对现有的CS压缩算法没有充分考虑信息的重要性差异,运用仿真手段验证了多分辨率压缩感知(Multiresolution CS,MCS)思想的正确性,仿真结果表明:MCS能够动态地保护信号中蕴含的重要信息,且与单一分辨率CS重构算法比较,精度明显提高。为下一步将MCS为直接信息采样提供软件支持。