基于压缩感知的差分关联成像方案研究

关联成像可提供一种运用常规手段难以获得清晰图像的方法, 能够解决一些常规成像技术不易解决的问题, 是近些年来量子光学领域的前沿和热点之一.本文提出一种基于压缩感知的差分关联成像方案(简称, 差分压缩关联成像方案), 将高斯分布的热光源强度分布作为压缩感知的测量矩阵, 差分物体信息作为被成像物体信息, 利用差分关联成像方案的高成像信噪比和压缩感知技术的低采样次数, 通过正交匹配追踪算法, 高质量地恢复出物体信息. 并以二灰度“双缝”、“NUPT”, 多灰度Lena图和Boats图为例, 数值仿真差分压缩关联成像过程; 同时将本方案350次测量的结果与差分关联成像方案30000次测量的结果进行对比, 研究结果表明针对不同的被成像物体(二灰度“双缝”、“NUPT”, 以及多灰度Lena图和Boats图), 10次成像的均方误差平均值分别降低了97.7%, 93.9%, 92.5%和71.4%; 与压缩鬼成像方案相比, 同样测量次数条件下均方误差值对于二灰度双缝和多灰度Lena图、Boats图等目标物 体分别有50.4%, 72.9%和66.8%的降低. 差分压缩关联成像方案极大地提高了成像信噪比, 降低了成像时间. 关键词： 关联成像 差分 压缩感知 均方误差     

基于lp范数的压缩感知图像重建算法研究

图像重建是光学成像、光声成像、声纳成像、核磁共振成像、 天体成像等物理成像领域中的关键技术之一. 近年来提出的压缩感知理论指出: 对稀疏或者可压缩信号进行少量非自适应线性投影,投影信号含有足够的信息, 从而能对信号进行高概率重建. 压缩感知已被应用于多种物理成像系统. 将罚函数法和修正Hesse阵序列二次规划方法相结合, 并采用了分块压缩感知思想, 提出一种基于l_p范数的压缩感知图像重建算法. 以cameraman, barbara和mandrill图像为例, 采用该算法进行图像重建. 首先, 在不同采样率下对图像重建. 即便采样率低至0.3时, 也能获得高达32.23dB的信噪比, 重建图像清晰可辨. 验证了该算法的正确性. 其次, 将该算法与正交匹配追踪算法进行对比, 在采样率达到0.5以上时, 能够获得高信噪比的重建图像, 成像时间也大为减少, 特别是采样率为0.7时, 成像时间减少88%. 最后, 与现有基于l_p 范数的压缩感知图像重建算法进行对比, 计算结果表明在成像质量有所提高的基础上, 成像时间大为缩短. 关键词： 图像重建 压缩感知 罚函数 修正Hesse阵序列二次规划     

Double-threshold technique for achieving denoising in compressive imaging applications

Single-pixel cameras, which employ either structured illumination or image modulation and compressive sensing algorithms, provide an alternative approach to imaging in scenarios where the use of a detector array is restricted or difficult because of cost or technological constraints. In this work, we present a robust imaging method based on compressive imaging that sets two thresholds to select the measurement data for image reconstruction.The experimental and numerical simulation results show that the proposed double-threshold compressive imaging protocol provides better image quality than previous compressive imaging schemes. Faster imaging speeds can be attained using this scheme because it requires less data storage space and computing time. Thus,this denoising method offers a very effective approach to promote the implementation of compressive imaging in real-time practical applications.     

基于Hadamard矩阵优化排序的快速单像素成像

为提升单像素成像速度,提出了基于Hadamard矩阵优化排序的压缩采样解决方案.利用数值仿真和室外实验对提出的5种排序方法进行了对比分析.研究结果表明:按Haar小波变换系数绝对值排序时单像素成像效果最优,排序对应到Walsh序后可利用快速变换重建图像,速度达300帧/秒@64×64像素;最优排序下,采样率25%仍可重建图像,采样速度可提升4倍.针对排序方法与成像信噪比关系,从关联成像角度给出了其物理解释:测量基矩阵元邻域数值相等的区域面积等效于光场二阶相干面积,当光场二阶相干面积随测量基由大到小排序时成像效果最优.本文研究成果可用于提升单像素成像速度,具有实用价值.     

基于自适应阈值方法实现迭代降噪鬼成像

为了有效降低传统鬼成像中相关噪声对成像质量的影响,本文提出一种基于最佳阈值的迭代降噪鬼成像.首先在迭代降噪鬼成像的基础上,采用自适应阈值迭代法,在不需要目标先验信息的前提下,找到一个逼近传统鬼成像中相关噪声的阈值,根据得到的阈值构造噪声干扰项.为了每次迭代初值更接近原始目标的透射系数,对其进行二值化,降低重构图像背景噪声对迭代性能的影响.仿真以及实验结果表明,本文提出的方法与传统方法相比,视觉效果以及峰值信噪比值有明显提高.     

Structured sublinear compressive sensing via belief propagation

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with orthogonal matching pursuit (OMP) methods. For reduced-complexity greedy reconstruction schemes, we propose a new family of list-decoding belief propagation algorithms, as well as reinforced and multiple-basis belief propagation (BP) algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity–performance tradeoffs for very sparse signal vectors.     

Orthogonal-triangular decomposition ghost imaging

Ghost imaging (GI) offers great potential with respect to conventional imaging techniques. However, there are still some obstacles for reconstructing images with high quality, especially in the case that the orthogonal measurement matrix is impossible to construct. In this paper, we propose a new scheme based on the orthogonal-triangular (QR) decomposition, named QR decomposition ghost imaging (QRGI) to reconstruct a better image with good quality. In the scheme, we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases. (1) When the random measurement matrix is square, it can be firstly decomposed into an orthogonal matrix $\bm Q$ and an upper triangular matrix $\bm R$. Then let the off-diagonal values of $\bm R$ equal to 0.0, the diagonal elements of $\bm R$ equal to a constant $k$, where $k$ is the average of all values of the main diagonal, so the resulting measurement matrix can be obtained. (2) When the random measurement matrix is with full rank, we firstly compute its transpose, and followed with above QR operation. Finally, the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values. Both experimental and simulation results verify the feasibility of the proposed QRGI scheme. Moreover, the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI (TGI) and differential GI (DGI). Besides, in comparison with the singular value decomposition ghost imaging (SVDGI), the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI, while the computing time (the time consuming on the light patterns computation) is substantially shortened.     

Piecewise spectrally band-pass for compressive coded aperture spectral imaging

Coded aperture snapshot spectral imaging(CASSI) has been discussed in recent years. It has the remarkable advantages of high optical throughput, snapshot imaging, etc. The entire spatial-spectral data-cube can be reconstructed with just a single two-dimensional(2D) compressive sensing measurement. On the other hand, for less spectrally sparse scenes,the insufficiency of sparse sampling and aliasing in spatial-spectral images reduce the accuracy of reconstructed threedimensional(3D) spectral cube. To solve this problem, this paper extends the improved CASSI. A band-pass filter array is mounted on the coded mask, and then the first image plane is divided into some continuous spectral sub-band areas. The entire 3D spectral cube could be captured by the relative movement between the object and the instrument. The principle analysis and imaging simulation are presented. Compared with peak signal-to-noise ratio(PSNR) and the information entropy of the reconstructed images at different numbers of spectral sub-band areas, the reconstructed 3D spectral cube reveals an observable improvement in the reconstruction fidelity, with an increase in the number of the sub-bands and a simultaneous decrease in the number of spectral channels of each sub-band.     

Efficient implementation of x-ray ghost imaging based on a modified compressive sensing algorithm

Towards efficient implementation of x-ray ghost imaging (XGI), efficient data acquisition and fast image reconstruction together with high image quality are preferred. In view of radiation dose resulted from the incident x-rays, fewer measurements with sufficient signal-to-noise ratio (SNR) are always anticipated. Available methods based on linear and compressive sensing algorithms cannot meet all the requirements simultaneously. In this paper, a method based on a modified compressive sensing algorithm with conjugate gradient descent method (CGDGI) is developed to solve the problems encountered in available XGI methods. Simulation and experiments demonstrate the practicability of CGDGI-based method for the efficient implementation of XGI. The image reconstruction time of sub-second implicates that the proposed method has the potential for real-time XGI.     

针对多散斑图的差分压缩鬼成像方案研究

鬼成像方案实现所需设备、成像的质量以及成像所花的时间是决定鬼成像技术可实用化的重要因素. 本文提出一种针对多散斑图的差分压缩鬼成像方案. 该方案通过连续探测多个独立的散斑图, 降低了热光鬼成像方案对探测器高时间分辨力的要求; 通过采用差分方法, 抑制了背景噪声和其他噪声源的干扰; 通过使用压缩感知重建算法, 有效地降低了鬼成像所需时间并同时提升成像的质量. 数值仿真结果表明, 对于二灰度“N” 图, 本方案在8000次的采样情形下与多散斑图鬼成像方案35000次采样的结果相比, 均方误差降低了96.9%、峰值信噪比提升15.1 dB. 对于八灰度“Pepper”图, 本方案与多散斑图鬼成像方案相比, PSNR提升11.4 dB. 本方案可降低探测设备的要求、提高成像质量、降低重建时间, 具有广阔的应用前景.     

压缩感知重建数字同轴全息

数字重建是数字全息技术的关键步骤.传统的重建算法存在共轭像、聚焦物体与背景离焦物体相互干扰等问题.应用新兴的压缩感知技术,研究了全息图像的稀疏重建.基于衍射的线性运算,导出了利用压缩感知重建数字同轴全息三维空间的算法.利用该算法对颗粒的模拟全息图和数字显微全息实验全息图进行了重建,并将重建结果与传统的卷积重建结果进行了...     

Mask-based denoising scheme for ghost imaging

Ghost imaging(GI) is thought of as a promising imaging method in many areas. However, the main drawback of GI is the huge measurement data and low signal-to-noise ratio. In this paper, we propose a novel mask-based denoising scheme to improve the reconstruction quality of GI. We first design a mask through the maximum between-class variance(OTSU)method and construct the measurement matrix with speckle patterns. Then, the correlated noise in GI can be effectively suppressed by employing the mask. From the simulation and experimental results, we can conclude that our method has the ability to improve the imaging quality compared with traditional GI method.     

Improvement of the optical image reconstruction based on multiplexed quantum ghost images

Ghost imaging allows one to obtain information on an object from the spatial correlation function between photons propagating through or reflected from the object and photons of the reference arm. In this case, detection in the object arm is performed over the entire aperture of the beam and, therefore, it does not give information on the object. The reference beam does not interact with the object, but is recorded with a scanning point detector or a CCD array permitting the measurement of the spatial correlation function of photons in two arms. The use of multimode entangled quantum light beams by illuminating the object by one beam and orienting other beams to reference arms makes it possible to obtain simultaneously several ghost images (GIs). Cross correlations of multiplexed GIs (MGIs) are determined by eighth-order field correlation functions. A special algorithm is developed for calculating higher-order correlations of Bose operators. The presence of GI cross correlations is used for improving the quality of the reconstructed object’s image by their processing using the measurement reduction method. An example of the computer simulation of the image reconstruction by MGIs formed in the field of four-frequency entangled quantum states is considered. It is found that in this case the reduced GI has a signal-to-noise ratio several times higher than that of GIs.     

Compressive imaging based on multi-scale modulation and reconstruction in spatial frequency domain

Imaging quality is a critical component of compressive imaging in real applications. In this study, we propose a compressive imaging method based on multi-scale modulation and reconstruction in the spatial frequency domain. Theoretical analysis and simulation show the relation between the measurement matrix resolution and compressive sensing(CS)imaging quality. The matrix design is improved to provide multi-scale modulations, followed by individual reconstruction of images of different spatial frequencies. Compared with traditional single-scale CS imaging, the multi-scale method provides high quality imaging in both high and low frequencies, and effectively decreases the overall reconstruction error.Experimental results confirm the feasibility of this technique, especially at low sampling rate. The method may thus be helpful in promoting the implementation of compressive imaging in real applications.     

低信噪比下的二维联合线性布雷格曼迭代快速超分辨成像算法

针对实际逆合成孔径雷达(ISAR)成像时带宽有限、方位孔径稀疏的小角度回波数据条件下,常规算法的成像分辨率不高等问题,基于压缩感知理论,提出了一种低信噪比条件下的二维联合布雷格曼迭代快速ISAR超分辨成像算法.首先,将雷达回波构建为距离频域-方位多普勒域的二维稀疏表示模型,在此基础上,将二维超分辨成像问题转换为二维联合压缩感知的稀疏重构问题;其次,为了避免重构时向量化操作带来的复杂度,提出了二维联合布雷格曼迭代算法,为实现快速重构,将加权残量迭代、估计停滞步长与感知矩阵条件数优化三种加快收敛速度的思想相结合,既利用了布雷格曼迭代在低信噪比条件下的重构能力又能保证快速成像.最后仿真实验结果表明在欠采样和低信噪比条件下本文算法能够缩短成像时间,且具备更好的噪声鲁棒性.     

Distributed imaging using an array of compressive cameras

We describe a distributed computational imaging system that employs an array of feature specific sensors, also known as compressive imagers, to directly measure the linear projections of an object. Two different schemes for implementing these non-imaging sensors are discussed. We consider the task of object reconstruction and quantify the fidelity of reconstruction using the root mean squared error (RMSE) metric. We also study the lifetime of such a distributed sensor network. The sources of energy consumption in a distributed feature specific imaging (DFSI) system are discussed and compared with those in a distributed conventional imaging (DCI) system. A DFSI system consisting of 20 imagers collecting DCT, Hadamard, or PCA features has a lifetime of 4.8× that of the DCI system when the noise level is 20% and the reconstruction RMSE requirement is 6%. To validate the simulation results we emulate a distributed computational imaging system using an experimental setup consisting of an array of conventional cameras.     

Preconditioning for multidimensional TOMBO imaging

In this Letter, we propose a preconditioning method to improve the convergence speed of iterative reconstruction algorithms in a compact, multidimensional, compound-eye imaging system called the thin observation module by bound optics. The condition number of the system matrix is improved by using a preconditioner matrix. To calculate the preconditioner matrix, the system model is expressed in the frequency domain. The proposed method is simulated by using a compressive sensing algorithm called the two-step iterative shrinkage/thresholding algorithm. The results showed improved reconstruction fidelity with a certain number of iterations for high signal-to-noise ratio measurements.     

Compressed imaging system with linear sensors

This Letter presents a new approach for imaging using a linear (vector) sensor. It exploits the fact that visual information within common human intelligible images may be compressed within only a partial set of radial strips of its Fourier domain. We present two imaging schemes, one coherent and the other incoherent, that capture the partial set of radial strips of the object Fourier domain. Two main advantages of the new approach are that the image is captured directly in a compressed form and that the acquisition time is shorter compared with conventional scanning imaging systems.     

鬼成像中一些数学问题

鬼成像是一种与传统成像方式不同的通过光场涨落的高阶关联获得图像信息的新型成像方式。近年来,相比传统成像方式,鬼成像所拥有的一些优点如高灵敏度、超分辨能力、抗散射等,使其在遥感、多光谱成像、热X射线衍射成像等领域得到广泛研究。随着对鬼成像的广泛研究,数学理论和方法在其中发挥的作用愈显突出。例如,基于压缩感知理论,可以进行鬼成像系统采样方式优化、图像重构算法设计及图像重构质量分析等研究工作。本文旨在探索鬼成像中的一些有趣的数学问题,主要包括:系统预处理方法、光场优化及相位恢复问题。对这些问题的研究既可以丰富鬼成像理论,又能推动它在实际应用中的发展。     

Image Encryption Scheme Based on Mixed Chaotic Bernoulli Measurement Matrix Block Compressive Sensing

Many image encryption schemes based on compressive sensing have poor reconstructed image quality when the compression ratio is low, as well as difficulty in hardware implementation. To address these problems, we propose an image encryption algorithm based on the mixed chaotic Bernoulli measurement matrix block compressive sensing. A new chaotic measurement matrix was designed using the Chebyshev map and logistic map; the image was compressed in blocks to obtain the measurement values. Still, using the Chebyshev map and logistic map to generate encrypted sequences, the measurement values were encrypted by no repetitive scrambling as well as a two-way diffusion algorithm based on GF(257) for the measurement value matrix. The security of the encryption system was further improved by generating the Secure Hash Algorithm-256 of the original image to calculate the initial values of the chaotic mappings for the encryption process. The scheme uses two one-dimensional maps and is easier to implement in hardware. Simulation and performance analysis showed that the proposed image compression–encryption scheme can improve the peak signal-to-noise ratio of the reconstructed image with a low compression ratio and has good encryption against various attacks.