基于压缩感知的加权宽带谱重构算法

压缩感知利用宽带无线信号的频域稀疏特性,能够在低于奈奎斯特速率的采样下利用少量观测数据实现宽带频谱估计和空穴检测。但相关频谱压缩感知算法的性能并不理想,为了实现宽带信道的快速准确感知,本文基于宽带信道的时频统计特性,在去噪基追踪算法(BPDN)的基础上提出了一种优化的加权去噪算法(WBPDN)。该算法利用子频段历史平均功率密度水平来构建各子频段权重以优化目标函数,改善算法性能。实验结果表明:该算法能通过少量观测数据准确重构宽带信道的谱估计,且比传统的BPDN和OMP算法具有更好的压缩性能及更小的重构误差;另外加权后的算法收敛速度更快,显著减少了算法所需的运行时间。      

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.     

基于重加权近似消息传递算法的稀疏信道估计

基于近似消息传递(AMP)算法,提出了一种重加权近似消息传递(Rw AMP)算法用于稀疏信道估计,该算法增加了重加权过程与衰减机制。在信号重构时加入权重更新过程,待重构信号中较大的元素几乎不变,较小元素迅速降低为零,从而提高正确重构概率。其次,当稀疏信道估计的观测矩阵为Toeplitz矩阵时,为了提高AMP类算法收敛性,文中加入衰减机制。仿真结果表明,在相同复杂度的条件下,Rw AMP算法的信号重构性能优于基追踪(BP)算法和AMP算法。     

Model-guided measurement-side control for quantized block compressive sensing

To progressively provide the competitive rate-distortion performance for aerial imagery,a quantized block compressive sensing(QBCS) framework is presented,which incorporates two measurement-side control parameters:measurement subrate(S) and quantization depth(D).By learning how different parameter combinations may affect the quality-bitrate characteristics of aerial images,two parameter allocation models are derived between a bitrate budget and its appropriate parameters.Based on the corresponding allocation models,a model-guided image coding method is proposed to pre-determine the appropriate(S,D) combination for acquiring an aerial image via QBCS.The data-driven experimental results show that the proposed method can achieve near-optimal quality-bitrate performance under the QBCS framework.     

Bayesian compressive sensing for cluster structured sparse signals

In traditional framework of compressive sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called model-based compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian compressive sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically—prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.     

Image representation by compressive sensing for visual sensor networks

This paper addresses the image representation problem in visual sensor networks. We propose a new image representation method for visual sensor networks based on compressive sensing (CS). CS is a new sampling method for sparse signals, which is able to compress the input data in the sampling process. Combining both signal sampling and data compression, CS is more capable of image representation for reducing the computation complexity in image/video encoder in visual sensor networks where computation resource is extremely limited. Since CS is more efficient for sparse signals, in our scheme, the input image is firstly decomposed into two components, i.e., dense and sparse components; then the dense component is encoded by the traditional approach (JPEG or JPEG 2000) while the sparse component is encoded by a CS technique. In order to improve the rate distortion performance, we leverage the strong correlation between dense and sparse components by using a piecewise autoregressive model to construct a prediction of the sparse component from the corresponding dense component. Given the measurements and the prediction of the sparse component as initial guess, we use projection onto convex set (POCS) to reconstruct the sparse component. Our method considerably reduces the number of random measurements needed for CS reconstruction and the decoding computational complexity, compared to the existing CS methods. In addition, our experimental results show that our method may achieves up to 2 dB gain in PSNR over the existing CS based schemes, for the same number of measurements.     

Image representation using block compressive sensing for compression applications

The emerging compressive sensing (CS) theory has pointed us a promising way of developing novel efficient data compression techniques, although it is proposed with original intention to achieve dimension-reduced sampling for saving data sampling cost. However, the non-adaptive projection representation for the natural images by conventional CS (CCS) framework may lead to an inefficient compression performance when comparing to the classical image compression standards such as JPEG and JPEG 2000. In this paper, two simple methods are investigated for the block CS (BCS) with discrete cosine transform (DCT) based image representation for compression applications. One is called coefficient random permutation (CRP), and the other is termed adaptive sampling (AS). The CRP method can be effective in balancing the sparsity of sampled vectors in DCT domain of image, and then in improving the CS sampling efficiency. The AS is achieved by designing an adaptive measurement matrix used in CS based on the energy distribution characteristics of image in DCT domain, which has a good effect in enhancing the CS performance. Experimental results demonstrate that our proposed methods are efficacious in reducing the dimension of the BCS-based image representation and/or improving the recovered image quality. The proposed BCS based image representation scheme could be an efficient alternative for applications of encrypted image compression and/or robust image compression.     

An efficient optimization of measurement matrix for compressive sensing

Compressive sensing (CS) is a new paradigm for signal acquisition and reconstruction, which can reconstruct the signal at less than the Nyquist sampling rate. The sampling of the signal occurs through a measurement matrix (MM); thus, MM generation is significant in the context of the CS framework. In this paper, an optimization algorithm is introduced for the generation of the MM of CS based on Restricted Isometric Property (RIP) mandates that eigenvalues of the sensing matrix fall within an interval also minimizes the mutual coherence of the sensing matrix (i.e. the product of the MM and sparsifying matrix). A novel gradient-based iterative optimization method is used to reduce the eigenvalues of the sensing matrix by SVD decomposition. Meanwhile, the proposed algorithm can also reduce the operational complexity. Experimental results and analysis prove that the optimized MM reduces the maximum mutual and average mutual coherence between the MM and the sparsifying basis, which shows the effectiveness of the proposed algorithm over some state-of-art works.     

Compression method for non-stationary signals based on compressive sensing

A new approach to compress non-stationary signals is proposed in this paper. The sparse basis of non-stationary signals is constructed at first and then compressive sensing technique is used to decrease enormously the number of samples in the process. The reconstructed signal can well approximate the original signal in time domain, frequency domain as well as the time-frequency domain. Computer simulation on linear frequency modulated (LFM) signal shows the validity of this novel method.     

Denoising recovery for compressive sensing based on selective measure

In order to reduce the effect of noise folding (NF) phenomenon on the performance of sparse signal recon-struction,a new denoising recovery algorithm based on selective measure was proposed.Firstly,the NF phenomenon in compressive sensing (CS) was explained in theory.Secondly,a new statistic based on compressive measurement data was proposed,and its probability density function (PDF) was deduced and analyzed.Then a noise filter matrix was constructed based on the PDF to guide the optimization of measurement matrix.The optimized measurement matrix can selectively sense the sparse signal and suppress the noise to improve the SNR of the measurement data,resulting in the improvement of sparse reconstruction performance.Finally,it was pointed out that increasing the measurement times can further enhance the performance of denoising reconstruction.Simulation results show that the proposed denoising recon-struction algorithm has a better improvement in the performance of reconstruction of noisy signal,especially under low SNR.     

A posteriori quantization of progressive matching pursuit streams

This paper proposes a rate-distortion optimal a posteriori quantization scheme for matching pursuit (MP) coefficients. The a posteriori quantization applies to an MP expansion that has been generated offline and cannot benefit of any feedback loop to the encoder in order to compensate for the quantization noise. The redundancy of the MP dictionary provides an indicator of the relative importance of coefficients and atom indices and, subsequently, on the quantization error. It is used to define a universal upper bound on the decay of the coefficients, sorted in decreasing order of magnitude. A new quantization scheme is then derived, where this bound is used as an Oracle for the design of an optimal a posteriori quantizer. The latter turns the exponentially distributed coefficient entropy-constrained quantization problem into a simple uniform quantization problem. Using simulations with random dictionaries, we show that the proposed exponentially upper bounded quantization (EUQ) clearly outperforms classical schemes. Stepping on the ideal Oracle-based approach, a suboptimal adaptive scheme is then designed that approximates the EUQ but still outperforms competing quantization methods in terms of rate-distortion characteristics. Finally, the proposed quantization method is studied in the context of image coding. It performs similarly to state-of-the-art coding methods (and even better at low rates) while interestingly providing a progressive stream that is very easy to transcode and adapt to changing rate constraints.     

率失真优化的压缩感知图像编码

针对基于压缩感知的图像编码系统,分析了系统中编码参数和码率以及失真的关系,在此基础上提出了基于压缩感知的图像编码系统的码率-失真模型.根据所提模型设计了率失真优化的压缩感知图像编码算法.在给定码率的条件下,优化编码参数,使得编码器失真最小.算法在Matlab的编码平台上进行了仿真和实验,结果证明提出的码率-失真模型能够很好地拟合实际率失真曲线,并且基于该模型的率失真优化算法有效的提高了压缩感知图像编码系统的性能.     

压缩感知图像融合

目前图像融合的方法大多数都是基于小波变换的图像融合方法,通过对小渡变换之后的低频系数和高频系数分别采用不同的融合准则,来达到所需要的图像以进行下一步处理,这些方法需要知道原始图像,也就是对硬件要求较高。采用压缩感知图像融合,即,将压缩感知用于图像融合,使得只知道原始图像在某个变换下的投影值的情况下,通过对已知的投影值使用融合规则得到融合后的投影值,然后用重构算法重构出图像,大大降低了对硬件的要求。在此给出了压缩感知融合方法与基于小波变换的图像融合方法的实验结果,融合结果表明,在不降低融合效果和视觉效果的基础上,该方法能够极大地降低硬件成本。采用熵作为衡量融合效果的指标,并对用两种方法融合的结果图像做了对比,研究结果表明,CS融合方法要优于基于小渡变换的图像融合方法。     

基于压缩感知的信号重构

压缩感知是针对稀疏或可压缩信号,在采样的同时即可对信号数据进行适当压缩的新理论,采用该理论,可以仅需少量信号的观测值来实现精确重构信号。文中概述了CS理论框架及关键技术问题,介绍了信号稀疏表示、观测矩阵和重构算法。最后仿真实现了基于压缩感知的信号重构,并对正交匹配追踪(OMP)重构算法性能作了分析。     

基于压缩感知的高光谱遥感影像重构方法研究

高光谱遥感影像包含丰富的空间、辐射以及光谱信息,同时海量的数据也引发了高光谱成像技术在传输和存储方面的诸多问题。针对这一问题,根据高光谱遥感影像谱间相关性强的特性,提出了一种结合谱间多向预测的基于压缩感知的高光谱遥感影像重构方法。首先,根据高光谱遥感影像的谱间相关性对高光谱遥感影像的波段进行分组,每组确定一个参考波段,使用平滑l_0范数算法重构每组的参考波段。其次,根据重构恢复的相邻组内的参考波段,建立了一个非参考波段预测模型,用来计算非参考波段的预测测量值;然后,计算实际测量值与预测测量值的差值,使用SL0算法重构该差值得到差值向量;最后,利用得到的差值向量迭代更新预测测量值,直到恢复该波段原始图像。仿真实验结果表明,该方法提高了高光谱遥感影像的重构效果。     

Adaptive interference suppression for DSSS communications based on compressive sensing

The existing interference suppression algorithms for direct sequence spread spectrum (DSSS) communications are confined to the high sampling rate. The compressive sensing is addressed to solve the problem in this paper. Firstly, the mathematical model of interference suppression in compressed domain is introduced; the DSSS signal and interference sparse dictionary is built. Secondly, according to the difficulty in obtaining the prior information of the interference signal sparse degree, the adaptive interference suppression algorithm is proposed by setting the reasonable control threshold. A comprehensive analysis and comparison of the algorithm are presented and discussed. The numerical experiments are provided to demonstrate the effectiveness of the proposed algorithm. The results show that the algorithm could suppress the interference effectively; the interference suppression performance does not change with the interference intensity and interference quantity. This will provide an effective method for the reconstruction of the compressed DSSS signal under the scenario of interference. The results obtained here may also be applicable in alternative spread spectrum technologies, like code division multiple access system.     

Non-reconstruction compressive detector for wideband spectrum sensing based on GLRT

Spectrum sensing is an essential ability to detect spectral holes in cognitive radio (CR) networks. The critical challenge to spectrum sensing in the wideband frequency range is how to sense quickly and accurately. Compressive sensing(CS) theory can be employed to detect signals from a small set of non-adaptive, linear measurements without fully recovering the signal. However, the existing compressive detectors can only detect some known deterministic signals and it is not suitable for the time-varying amplitude signal, such as spectrum sensing signals in CR networks. First, a model of signal detect is proposed by utilizing compressive sampling without signal recovery, and then the generalized likelihood ratio test (GLRT) detection algorithm of the time-varying amplitude signal is derived in detail. Finally, the theoretical detection performance bound and the computation complexity are analyzed. The comparison between the theory and simulation results of signal detection performance over Rayleigh and Rician channel demonstrates the validity of the performance bound. Compared with the reconstructed spectrum sensing detection algorithm, the proposed algorithm greatly reduces the data volume and algorithm complexity for the signal with random amplitudes.     

A compressive sensing and unmixing scheme for hyperspectral data processing

Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation, and input/output throughputs, particularly when real-time processing is desired. In this paper, a proof-of-concept study is conducted on compressive sensing (CS) and unmixing for hyperspectral imaging. Specifically, we investigate a low-complexity scheme for hyperspectral data compression and reconstruction. In this scheme, compressed hyperspectral data are acquired directly by a device similar to the single-pixel camera based on the principle of CS. To decode the compressed data, we propose a numerical procedure to compute directly the unmixed abundance fractions of given endmembers, completely bypassing high-complexity tasks involving the hyperspectral data cube itself. The reconstruction model is to minimize the total variation of the abundance fractions subject to a preprocessed fidelity equation with a significantly reduced size and other side constraints. An augmented Lagrangian-type algorithm is developed to solve this model. We conduct extensive numerical experiments to demonstrate the feasibility and efficiency of the proposed approach, using both synthetic data and hardware-measured data. Experimental and computational evidences obtained from this paper indicate that the proposed scheme has a high potential in real-world applications.     

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.