基于块稀疏度与自适应迭代的压缩感知方法

针对分块压缩感知算法在平滑块效应时损失了大量的细节纹理信息,从而影响图像的重构效果问题,提出了一种基于块稀疏信号的压缩感知重构算法。该算法先采用块稀疏度估计对信号的稀疏性做初步估计,通过对块稀疏度进行估算初始化阶段长,运用块矩阵与残差信号最匹配原则来选取支撑块,再运用自适应迭代计算实现对块稀疏信号的重构,较好地解决了浪费存储资源和计算量大的问题。实验结果表明,相比常用压缩感知方法,所提算法能明显减少运算时间,且能有效提高图像重构效果。     

C-RAN网络中基于稀疏性的预测矩阵求解算法

在C-RAN（Centralized,Cooperative,Cloud Radio Access Network）无线网络基于转移矩阵的负载预测方法中,虽然该预测矩阵具有稀疏特性,但是现有的技术缺乏对稀疏特性加以利用,从而造成计算复杂。针对此问题,提出了一种基于稀疏性的预测矩阵求解算法。该算法对网络状态转移矩阵进行分块迭代,每次等分4块,并分别定义4块矩阵的偏移量。当属于同一行的块矩阵的偏移量有一个是零矩阵时,直接得出所求矩阵对应块的元素全部为零,然后进行下一次迭代;当属于同一行的块矩阵偏移量都不为零矩阵时,通过对矩阵方程组变形处理,转换成迭代格式,然后分块处理。最后,结合仿真定量分析稀疏矩阵稀疏度的临界值问题,给出了稀疏度与计算量之间的关系,并证明了其合理性。仿真结果表明,所提算法能够在不影响预测准确度前提下,降低复杂度。     

基于块稀疏贝叶斯学习的SAR图像目标方位角估计方法

提出了一种基于块稀疏贝叶斯学习的合成孔径雷达（Synthetic aperture radar,SAR）图像目标方位角估计方法。SAR图像具有较强的方位角敏感性,因此对于具有某一方位角的SAR图像仅能与其具有相近方位角的样本具有较高的相关性。方法基于稀疏表示的基本思想,首先对所有训练样本按照方位角顺序排列为全局字典。在此条件下,待估计样本在该字典上的线性表示系数具有块稀疏特性,即非零表示系数主要聚集在字典上的某一局部区域。求解得到的块稀疏位置包含的训练样本可以有效地反映待估计样本的方位角信息。采用块稀疏贝叶斯学习（Block sparse Bayesian learning, BSBL）算法求解全局字典上的稀疏表示系数,并根据具有最小重构误差的原则获得最佳的局部分块。在获取最佳分块的基础上,方位角计算方法采用线性加权的方式综合了该分块区间内所有训练样本的方位角信息从而获得更为稳健的估计结果。所提出的方法在充分考察SAR图像方位角敏感性的基础上,综合运用局部区间内样本的有效信息,避免了基于单一样本估计的不确定性。为了验证所提出方法的有效性,基于Moving and stationary target acquisition and recognition （MSTAR）数据集进行了方位角估计实验并与几类经典方法进行对比分析。实验结果验证了所提出方法的性能优势。     

一种分块自适应压缩感知图像重构算法

CS理论中,在离散余弦变换下使用OMP算法重构图像时需要较高的测量值可以获得较好的重构效果,但是存在重构图像模糊的问题.为此,提出了基于离散余弦变换的图像分块自适应正交匹配追踪(BAD-OMP)算法.基于分块压缩感知技术,对图像进行均匀分块处理,根据图像块稀疏性进行自适应采样,再用均值滤波算法平滑处理,从而减少重构所需的测量值,降低块效应.仿真结果表明,采样率取0.1 ～0.35 时,BAD-OMP算法重构图像的PSNR值较OMP算法的PSNR值高9～1 1 dB,实现了在低采样率下获得较高的重构质量.     

图像分块压缩感知中的自适应测量率设定方法

传统的图像分块压缩感知(BCS, block compressed sensing)以相同的测量率对各块进行测量,但由于图像的空间特性不同,在重构图像时出现了块效应。通过自适应为各块设定不同的测量率,该问题可得到有效的解决。然而,已有的自适应测量率设定法需要在采集端获得原始数字图像,这在实际的压缩成像(CI, compressive imaging)设备中无法实现。为了克服这一缺陷,提出了一种更易于通过硬件实现的自适应测量率设定法。该方法利用在采集端可获得的CS测量值直接在测量域中估计各图像块的样本方差,再根据各块样本方差自适应地为每块设定测量率并实现码率控制。仿真实验结果表明,该方案重构图像的质量优于非自适应方案,但由于测量域估计块样本方差存在偏差,使其与直接利用块样本方差真实值的自适应方案相比,仍具有一定差距。     

面向压缩感知的块稀疏度自适应迭代算法

块稀疏信号是一种典型的稀疏信号,目前在块稀疏信号的压缩感知问题中,大多数信号重构算法要求信号的块稀疏度已知且算法复杂度高.针对实际应用中信号块稀疏度未知的情况,提出了一种块稀疏度自适应迭代算法,用于信号重构.首先,该算法初始化一个块稀疏度,其值按设定步长进行增加.对每一个块稀疏度的迭代,算法都会找到信号支撑块的一个子集,并修正更新上一次找到的信号支撵块,最后找到信号的整个支撑块,从而重构出源信号.该算法不需要信号的块稀疏度作为先验知识,而且算法复杂度低.仿真实验表明,该算法的重构概率较已有大多数块稀疏信号重构算法的重构概率高,在块稀疏信号的压缩感知问题中具有实际意义.     

基于信息辅助块稀疏贝叶斯学习的直扩通信窄带干扰抑制

现有基于Nyquist-Shannon采样定理的窄带干扰(Narrowband Interference,NBI)抑制方法存在应用受限于采样率较高的问题。应用压缩感知(Compressive Sensing,CS)理论解决上述问题,利用NBI在频域表现出的块稀疏特性以及直接序列扩频(Direct Sequence Spread Spectrum,DSSS)信号的类噪声特性,提出了基于块稀疏贝叶斯学习(Block Sparse Bayesian Learning,BSBL)框架的DSSS通信NBI抑制模型。实现干扰抑制后,利用传统的CS重构算法实现DSSS信号的压缩域解调。为进一步提高算法性能,将NBI稀疏分块的块内自相关矩阵建模为单位矩阵,提出了信息辅助BSBL(Aid BSBL,ABSBL)算法,设计了基于ABSBL的DSSS通信NBI抑制算法。该算法在保持较好NBI抑制性能的条件下,提高了运算效率并且不依赖NBI的稀疏结构。仿真验证和对比分析结果表明,所提方法能够有效抑制DSSS通信中的NBI,在干扰强度相同的条件下,NBI带宽越小、压缩率越大,算法对NBI的抑制性能越好。     

基于最佳线性估计的快速压缩感知图像重建算法

针对目前存在的压缩感知(CS)重建算法计算复杂度过高的问题,该文提出一种基于最佳线性估计的快速CS图像重建算法。该算法在编码端进行分块自适应CS随机测量,在解码端根据图像块不同的统计特性,估计出统计自相关函数矩阵,进而构造出最佳线性算子用于重建出各个图像块。由于该算法用线性投影的方式替代了传统CS重建算法的非线性迭代过程,使得其大大缩短了图像重建时间。仿真实验结果表明,对于纹理细节不复杂的图像,所提出的算法并没有因为其计算复杂度的减少而影响到重建质量,仍优于目前流行的CS重建算法。     

基于自适应分块的高光谱图像压缩感知重构方法

在对高光谱图像采样重构的研究中，整体采样和固定分块采样没有考虑到高光谱图像复杂的纹理特征分布，使用了相同的测量矩阵导致图像的重构质量较差。针对此问题，该文提出基于2维图像熵自适应分块压缩感知重构方法(ABCS-IE)，该方法以图像2维熵作为高光谱图像纹理细节的度量，根据图像的纹理细节分布自适应改变图像子块的大小，然后为不同的图像块分配特定的采样值，根据分配的采样值设计专有的测量矩阵对图像块进行压缩测量，将采样测量值代入重构算法中进行重构。实验结果表明，与整体采样重构和固定分块采样重构相比，将该方法应用到压缩感知重构算法中对高光谱图像进行采样重构后，重构的图像在视觉效果上有明显的提高，取得的峰值信噪比(PSNR)和结构相似度(SSIM)最大，采样率为0.4时，PSNR提高了2～4 dB,SSIM最大提高了0.27，均方根误差(RMSE)和信息熵差值(ΔH)也有所降低，说明重构的图像更加接近原始图像。而且运算时间也减少了1～1.5 s。可见，该方法能充分利用高光谱图像的纹理特征，有效提高图像的重构质量，同时减少重构的运算时间。     

基于块压缩感知的SAR层析成像方法

基于压缩感知(Compressive Sensing, CS)的SAR层析成像方法(SAR Tomography, TomoSAR),虽然实现了对目标的3维重构,但对于具有结构特性的目标其重构性能较差。针对这一问题,该文提出了采用块压缩感知(Block Compressive Sensing, BCS)算法,该方法首先在CS方法基础上将具有结构特性的目标信号重构问题转化为BCS问题,然后根据目标结构特性与雷达参数的关系确定块的大小,最后对目标进行块稀疏的l1/l2范数最优化求解。相比基于CS的SAR层析成像方法,该方法更好地利用了目标的稀疏特性和结构特性,其重构精度更高、性能更优。仿真数据和Radarsat-2星载SAR实测数据的试验结果验证了该方法的有效性。      

Image compressed sensing based on wavelet transform in contourlet domain

Compressed sensing (CS) has been widely concerned and sparsity of a signal plays a crucial role in CS to exactly recover signals. Contourlet transform provides sparse representations for images, so an algorithm of CS reconstruction based on contourlet is considered. Meanwhile, taking into account the computation and the storage of large random measurement matrices in the CS framework, we are trying to introduce the wavelet transform into the contourlet domain to reduce the size of random measurement matrices. Several numerical experiments demonstrate that this idea is feasible. The proposed algorithm possesses the following advantages: reduced size of random measurement matrix and improved recovered performance.     

Fast reconstruction method for compressed sensing model with semi-tensor product

To reduce the storage space of random measurement matrix and improve the reconstruction efficiency for compressed sensing (CS),a new sampling approach for CS with semi-tensor product (STP-CS) was proposed.The proposed approach generated a low dimensional random measurement matrix to sample the sparse signals.Then the solutions of the sparse vector were estimated group by group with a l_q-minimization (0$\frac{M}{t}\text{×}\frac{N}{t}$ and decrease tow orders of magnitude of time that for conventional CS,while maintaining the reconstruction quality.Numerical results also show that the reconstruction time can be effectively improved 260 for the image size of 1 024×1 024.     

分块的有序范德蒙矩阵作为压缩感知测量矩阵的研究

测量矩阵是压缩感知(Compressed Sensing, CS)的重要组成部分,确定性的测量矩阵易于硬件实现,但是重构信号的精度一般不如随机矩阵。针对这一缺点,该文提出并构造了一种新的确定性测量矩阵,称作分块的有序范德蒙矩阵。范德蒙矩阵具有线性不相关的性质,在此基础上加上分块操作和对元素进行有序排列得到的分块的有序范德蒙矩阵,实现了时域中的非均匀采样,特别适合于维数较大的自然图像信号。仿真实验表明,对于图像信号该矩阵具有远高于高斯矩阵的重构精度,可以作为实际中的测量矩阵使用。     

基于稀疏度自适应压缩感知的电容层析成像图像重建算法

为提高电容层析成像(ECT)系统重建图像的质量,该文提出一种基于改进稀疏度自适应的压缩感知电容层析成像算法。利用压缩感知与电容层析成像算法的契合点,以随机改造后的电容层析成像灵敏度矩阵为观测矩阵,离散余弦基为稀疏基,测量电容值为观测值,建立模型。利用线性反投影算法(LBP算法)所得图像预估原始图像稀疏度,以预估稀疏度值作为索引原子初始值进行稀疏度自适应迭代。改进后的稀疏度自适应匹配追踪重构算法实现ECT图像重建,解决了稀疏度预估不准确导致重建图像精度差的问题。仿真实验结果表明,该算法可以有效重建ECT图像,其成像质量优于LBP算法、Landweber算法、Tikhonov算法等传统算法,是研究电容层析成像图像重建的一种新的方法和手段。     

Clustering compressed sensing based on image block similarities

Compressed sensing （CS） algorithm enables sampling rates significantly under classical Nyquist rate without sacrificing reconstructed image quality. It is known that, a great number of images have many similar areas which are composed by the same number of grayscale or color. A new CS scheme, namely clustering compressed sensing （CCS）, was proposed for image compression, and it introduces clustering algorithm onto framework of CS based on similarity of image blocks. Instead of processing the image as a whole, the image is firstly divided into small blocks, and then the clustering algorithm was proposed to cluster the similar image blocks. Afterwards, the optimal public image block in each category is selected as the representative for transmission. The discrete wavelet transform （DWT） and Gaussian random matrix are applied to each optimal public image block to obtain the random measurements. Different from equal measurements, the proposed scheme adaptively selects the number of measurements based on different sparsity of image blocks. In order to further improve the performance of the CCS algorithm, the unequal-CCS algorithm based on the characteristics of wavelet coefficients was proposed as well. The low frequency coefficients are retained to ensure the quality of reconstructed image, and the high frequency coefficients are compressed by the CCS algorithm. Experiments on images demonstrate good performances of the proposed approach.     

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.     

iPiano-Net: Nonconvex optimization inspired multi-scale reconstruction network for compressed sensing

Compressed sensing (CS) aims to precisely reconstruct the original signal from under-sampled measurements, which is a typical ill-posed problem. Solving such a problem is challenging and generally needs to incorporate suitable priors about the underlying signals. Traditionally, these priors are hand-crafted and the corresponding approaches generally have limitations in expressive capacity. In this paper, a nonconvex optimization inspired multi-scale reconstruction network is developed for block-based CS, abbreviated as iPiano-Net, by unfolding the classic iPiano algorithm. In iPiano-Net, a block-wise inertial gradient descent interleaves with an image-level network-inducing proximal mapping to exploit the local block and global content information alternately. Therein, network-inducing proximal operators can be adaptively learned in each module, which can efficiently characterize image priors and improve the modeling capacity of iPiano-Net. Such learned image-level priors can suppress blocky artifacts and noises/corruptions while preserving the global information. Different from existing discriminative CS reconstruction models trained with specific measurement ratios, an effective single model is learned to handle CS reconstruction with several measurement ratios even the unseen ones. Experimental results demonstrate that the proposed approach is substantially superior to previous CS methods in terms of Peak Signal to Noise Ratio (PSNR) and visual quality, especially at low measurement ratios. Meanwhile, it is robust to noise while maintaining comparable execution speed.     

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。     

半张量积低存储压缩感知方法研究

由于随机观测矩阵的随机性,存在数据存储量大、内存占用率高、数据计算量大以及难以面向大规模实际应用等问题.为此,提出了一种可有效降低随机观测矩阵所占存储空间的半张量积压缩感知（STP-CS）方法.利用该方法,构建低维随机观测矩阵,经奇异值分解（SVD）优化后对原始信号进行采样,并利用拟合0-范数的迭代重加权方法进行重构.实验利用2维灰度图像进行测试,并对重构图像的峰值信噪比,结构相似度等指标进行了统计和比较.实验结果表明,本文所述的STP-CS方法在不改变随机观测矩阵数据类型的前提下,可将观测矩阵减小至传统CS模型中观测矩阵所占内存空间的1/256（甚至更低）,同时仍保持很高的重构质量.