CN103558606A

CN103558606A - Condition part measuring associated imaging method based on compressive sensing

Info

Publication number: CN103558606A
Application number: CN201310521865.8A
Authority: CN
Inventors: 赵生妹; 陈超; 庄鹏; 巩龙延; 白旭
Original assignee: Nanjing Post and Telecommunication University
Current assignee: Nanjing Post and Telecommunication University
Priority date: 2013-10-29
Filing date: 2013-10-29
Publication date: 2014-02-05

Abstract

The invention discloses a condition part measuring associated imaging method based on compressive sensing. According to the method, the compressive sensing (CS) is combined with the associated imaging method based on condition part measurement. On one hand, part condition measurement is adopted in the method, restored imaging data are reduced into a half of traditional associated imaging rebuilt data, and positive images and negative images can be given at the same time, and on the other hand, an advanced signal processing method (the compressive sensing) is used to rebuild image information of an object, so that less measuring data can be used to obtain the image information of the object through a convex optimal solution. Consequently, the method reduces imaging restoration time, improves imaging quality, and provides reference for practical associated imaging.

Description

A Conditional Partial Measurement Correlation Imaging Method Based on Compressed Sensing

技术领域technical field

本发明涉及一种基于压缩感知的关联成像方法的实现方法，研究内容属于通信信号处理及量子光学交叉技术领域。The invention relates to an implementation method of an associated imaging method based on compressed sensing, and the research content belongs to the technical fields of communication signal processing and quantum optics intersection.

背景技术Background technique

关联成像，又称为“鬼”成像（Ghost imaging，GI），是二十世纪九十年代逐渐发展起来的一种新型成像方式，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，可应用于卫星遥感，激光雷达，医学成像，军事，工业成像以及深空探测等多种领域，具有广泛的应用前景。传统关联成像在实现时，存在采样次数较多、成像时间长、成像质量有待提高等问题。获得既可减少关联成像的成像时间，又可提升关联成像的质量的新型关联成像方法，是关联成像可实用化的前提。Correlation imaging, also known as "ghost" imaging (Ghost imaging, GI), is a new imaging method gradually developed in the 1990s, which can provide a method that is difficult to obtain clear images by conventional means, and can solve Some problems that are not easily solved by conventional imaging technology can be applied to various fields such as satellite remote sensing, lidar, medical imaging, military, industrial imaging, and deep space exploration, and have broad application prospects. When traditional correlation imaging is implemented, there are problems such as high sampling times, long imaging time, and imaging quality that needs to be improved. Obtaining a new correlative imaging method that can reduce the imaging time of correlative imaging and improve the quality of correlative imaging is the prerequisite for the practical use of correlative imaging.

2012年，罗等人在赝热光关联成像基础上，提出一种基于条件部分测量的关联成像方法（Ghost imaging using conditioned partial measurements,简称CPMGI）。这种方法以物臂测量值为判决条件，仅利用参考臂的部分测量数据，完整地恢复出目标物体的像。它给出了一种关联成像的像信息可通过参考臂的测量值的线性叠加获得的新型思路。然而，尽管条件部分测量方法中像信息的恢复相对于常见关联成像方法有了测量次数的减少，但是仍面临数据量大、重建时间长、所需物理存储较多等问题。另一方面，基于压缩感知的关联成像可大大减小采样次数，缩短成像时间，且提高成像质量。因此，本发明将压缩感知理论（CompressiveSensing，CS）与基于条件部分测量关联成像方法相结合，提出一种基于压缩感知的条件部分测量关联成像方法（Compressive Conditioned partial measurements Ghost Imaging，CCPMGI），以进一步减少成像恢复方法的测量次数，降低了成像恢复时间，提高成像质量，因而具有重要的理论意义和应用价值。In 2012, Luo et al. proposed a correlation imaging method based on conditional partial measurements (Ghost imaging using conditioned partial measurements, CPMGI for short) based on pseudo-thermo-optic correlation imaging. This method takes the measurement value of the object arm as the judgment condition, and only uses part of the measurement data of the reference arm to completely restore the image of the target object. It gives a new way of thinking that the image information of correlated imaging can be obtained by the linear superposition of the measured values of the reference arm. However, although the recovery of image information in the conditional partial measurement method has reduced the number of measurements compared with the common correlation imaging method, it still faces problems such as large data volume, long reconstruction time, and more physical storage required. On the other hand, associated imaging based on compressed sensing can greatly reduce the sampling times, shorten the imaging time, and improve the imaging quality. Therefore, the present invention combines the compressed sensing theory (CompressiveSensing, CS) with the method based on conditional partial measurements correlation imaging, and proposes a conditional partial measurements correlation imaging method based on compressed sensing (Compressive Conditioned partial measurements Ghost Imaging, CCPMGI), to further Reducing the measurement times of the imaging recovery method reduces the imaging recovery time and improves the imaging quality, so it has important theoretical significance and application value.

发明内容Contents of the invention

本发明目的在于提供一种基于压缩感知的条件部分测量关联成像的实现方法，该方法采用了部分条件测量方法，它的采样数据约等于传统关联成像方法的采样数据的一半，且该方法可同时给出正图像和负图像；同时，该方法进一步采用先进的信号处理方法（压缩感知方法）来重建物体的像信息，可用更少的测量数据利用凸优解方法获得物体的像信息。因此，本发明为关联成像的实用化了提供参考方法。The purpose of the present invention is to provide a method for implementing conditional partial measurement correlation imaging based on compressed sensing. The method uses a partial conditional measurement method, and its sampling data is approximately equal to half of the sampling data of the traditional correlation imaging method, and the method can simultaneously A positive image and a negative image are given; at the same time, the method further uses an advanced signal processing method (compressed sensing method) to reconstruct the image information of the object, and the image information of the object can be obtained by using the convex optimal solution method with less measurement data. Therefore, the present invention provides a reference method for the practical application of correlation imaging.

技术方案：Technical solutions:

本发明解决其技术问题所采取的技术方案是：本发明基于压缩感知的条件部分测量赝热光源关联成像方法的示意图如图1所示，假设桶探测器D与赝热光源之间的光学距离为Z₁，CCD探测器距光源的光学距离为Z₂，且假设Z₁＝Z₂。赝热光源的出射光经过50：50分束器后，分成两支独立的光路。一支光路定义为参考臂,其光束在自由空间中传播至CCD探测器。每次CCD的探测值记为I_j(x,y)，其中j＝1,2,...,M，M为测量次数，且<I(x,y)>定义为

为参考臂CCD探测器M次测量后的均值；另一支光路定义为物臂，其光束透过空间分布为T(x,y)的物体后，由置于其后的桶探测器D接收，每次桶探测器D的探测值记为D_j，其中j＝1,2,...,M，共进行M次测量，其平均值<D>定义为

The technical solution adopted by the present invention to solve its technical problems is: the schematic diagram of the method for measuring the correlation imaging of pseudothermal light sources based on the conditional part of compressed sensing in the present invention is shown in Figure 1, assuming the optical distance between the barrel detector D and the pseudothermal light source is Z ₁ , the optical distance between the CCD detector and the light source is Z ₂ , and it is assumed that Z ₁ =Z ₂ . The outgoing light of the pseudothermal light source is divided into two independent optical paths after passing through a 50:50 beam splitter. One optical path is defined as the reference arm, and its beam propagates to the CCD detector in free space. The detection value of each CCD is recorded as I _j (x,y), where j=1,2,...,M, M is the number of measurements, and <I(x,y)> is defined as

is the mean value after M measurements of the CCD detector of the reference arm; the other optical path is defined as the object arm, and its beam passes through an object with a spatial distribution of T(x,y), and is received by the barrel detector D placed behind it , the detection value of each barrel detector D is recorded as D _j , where j=1,2,...,M, a total of M measurements are made, and the average value <D> is defined as

桶探测器D的每一个探测值D_j均与物体透射函数T(x，y)有关,即:Each detection value D _j of the barrel detector D is related to the object transmission function T(x, y), namely:

D_j＝∫T(x,y)I_j(x,y)dxdy,j＝1,…,M, (1)D _j =∫T(x,y)I _j (x,y)dxdy,j=1,...,M, (1)

基于赝热光源的关联成像二阶关联函数可表示为：The second-order correlation function of correlation imaging based on pseudothermal light source can be expressed as:

G⁽²⁾(x,y)＝G₀+|∫T(x′,y′)δ_xx′δ_yy′dx′dy′|²， (2)G ⁽²⁾ (x,y)＝G ₀ +|∫T(x′,y′)δ _xx′ δ _yy′ dx′dy′| ² ， (2)

其中，G₀为一个常数，它的归一化二阶关联函数为：Among them, G ₀ is a constant, and its normalized second-order correlation function is:

g⁽²⁾(x,y)＝1+|∫T(x′,y′)δ_xx′δ_yy′dx′dy′|²， (3)g ⁽²⁾ (x,y)=1+|∫T(x′,y′)δ _xx′ δ _yy′ dx′dy′| ² ， (3)

若在物臂和参考臂分别测量M次，根据计算关联成像方法，归一化的物臂和参考臂的交叉关联为

因此，物体的信息可表示为If the object arm and the reference arm are measured M times respectively, according to the computational correlation imaging method, the normalized cross-correlation between the object arm and the reference arm is

Therefore, the information of the object can be expressed as

$11 + + {| | T T ((x x,, y the y)) | |}^{22} = = \frac{11}{M m} {Σ Σ}_{j j = = 11}^{M m} \frac{{D D.}_{j j}}{< < D D. > >} \frac{{I I}_{j j} ((x x,, y the y))}{< < I I ((x x,, y the y)) > >},, - - - - - - ((44))$

即，Right now,

${| | T T ((x x,, y the y)) | |}^{22} = = \frac{11}{M m} {Σ Σ}_{j j = = 11}^{M m} ((\frac{{D D.}_{j j}}{< < D D. > >} - - 11)) \frac{{I I}_{j j} ((x x,, y the y))}{< < I I ((x x,, y the y)) > >} - - - - - - ((55))$

由此可见，赝热光源二阶关联成像中在参考臂中获得物体的像信息可由参考臂探测值I_j(x,y)与物臂探测值D_j的加权线性叠加获得。由于<D>、<I(x,y)>对于关联成像过程来说为一常量，因此物体像信息为分为正、负像信息，且可近似表示为It can be seen that the image information of the object obtained in the reference arm in the second-order correlation imaging of the pseudothermal light source can be obtained by the weighted linear superposition of the detection value I _j (x, y) of the reference arm and the detection value D _j of the object arm. Since <D> and <I(x,y)> are constants for the associated imaging process, the object image information is divided into positive and negative image information, which can be approximately expressed as

$&PlusMinus; &PlusMinus; {| | T T ((x x,, y the y)) | |}^{22} &cong; &cong; \frac{11}{M m} {Σ Σ}_{j j = = 11}^{M m} sgn sgn ((\frac{{D D.}_{j j}}{< < D D. > >} - - 11)) \frac{{I I}_{j j} ((x x,, y the y))}{< < I I ((x x,, y the y)) > >},, - - - - - - ((66))$

其中，in,

$\{\begin{matrix} + + 11,, & {D D.}_{j j} - - < < D D. > > > > 00;; \\ - - 11,, & {D D.}_{j j} - - < < D D. > > < < 00 . . \end{matrix} - - - - - - ((77))$

由此，物臂测量值均值<D>在参考臂中获得物体像信息过程中起到了门限判决作用。在N<M次测量情况下，物体像信息的正、负取决于

的符号。若将物臂测量值分成两部分，即高于<D>的部分，记为

而低于<D>的部分，记为

对应地，也将参考臂测量值即光场强度I_j(x,y)，分为I_j ⁺(x,y)和I_j ^-(x,y)；则正图像就是由所有{I_j ⁺(x,y)}的线性叠加获得的物体像信息；负图像则是由所有{I_j ^-(x,y)}线性叠加获得的物体像信息。直观上，正、负图像的重建过程与被重建的物体不相关，而仅依赖于参考臂中光场的正、负分布。因此，若物体的大小为n×n，则在参考臂中至少要有M=1/2×n×n次不同的强度分布图样才获得物体的正、负像。Therefore, the mean value <D> of the measured value of the object arm plays a threshold judgment role in the process of obtaining object image information in the reference arm. In the case of N<M measurements, the positive and negative information of the object image depends on

symbol. If the measured value of the object arm is divided into two parts, that is, the part higher than <D>, recorded as

And the part below <D> is recorded as

Correspondingly, the measured value of the reference arm, i.e. the light field intensity I _j (x, y), is also divided into I _j ⁺ (x, y) and I _j ^- (x, y); then the positive image consists of all {I _j ⁺ (x,y)} The object image information obtained by linear superposition; the negative image is the object image information obtained by all {I _j ^- (x,y)} linear superposition. Intuitively, the reconstruction process of positive and negative images is not related to the object being reconstructed, but only depends on the positive and negative distribution of the light field in the reference arm. Therefore, if the size of the object is n×n, there must be at least M=1/2×n×n different intensity distribution patterns in the reference arm to obtain the positive and negative images of the object.

然而，物体通常都具有稀疏性，即它们在一定变换基表示下只有少量的空间分布不为零，如图片在二维离散余弦变换(2Dimensional-discrete cosine transform,简记为2D-DCT)或小波变换(wavelet transform,简记为WT)下就具有强稀疏性。因此，可通过压缩感知重建方法获得条件部分测量赝热光源关联成像方法的正负图像。利用压缩感知重建方法关键在于获得相关的测量向量和测量矩阵，且要求测量矩阵与稀疏基互不相关。However, objects usually have sparsity, that is, they have only a small amount of spatial distribution that is not zero under a certain transformation base representation, such as pictures in two-dimensional discrete cosine transform (2Dimensional-discrete cosine transform, abbreviated as 2D-DCT) or wavelet Transform (wavelet transform, abbreviated as WT) has strong sparsity. Therefore, the positive and negative images of the conditional partial measurement pseudothermal light source correlation imaging method can be obtained by the compressed sensing reconstruction method. The key to using compressed sensing reconstruction method is to obtain the relevant measurement vector and measurement matrix, and the measurement matrix is required to be uncorrelated with the sparse basis.

赝热光源关联成像要求光场分布具有随机性，这满足了以光场分布构成的测量矩阵和物体稀疏基间的不相关性。假设对于参考臂中光束传播横截面上点(x,y),x,y＝1,…,n，M次测量中第j次测量时的光强度分布函数为I_j(x,y),j＝1,...,M，其矩阵形式为：Pseudothermal light source correlative imaging requires the randomness of the light field distribution, which satisfies the uncorrelation between the measurement matrix formed by the light field distribution and the sparse basis of the object. Assuming that for a point (x,y) on the beam propagation cross section in the reference arm, x,y=1,...,n, the light intensity distribution function at the jth measurement in the M measurements is I _j (x,y), j=1,...,M, its matrix form is:

其中

光束传播横截面上点(x,y),x,y＝1,…,n的光场分布大小。矩阵I_j大小为n×n，若将其按行展开成一维行向量，可以得到

M次测量后，取p个I_j ⁺(x,y)的光强度作为压缩感知恢复方法的测量矩阵，其中

压缩感知测量矩阵为：in

The size of the light field distribution at the point (x, y), x, y=1,...,n on the beam propagation cross section. The size of the matrix I _j is n×n, if it is expanded into a one-dimensional row vector by row, we can get

After M measurements, the light intensities of p I _j ⁺ (x, y) are taken as the measurement matrix of the compressive sensing recovery method, where

The compressed sensing measurement matrix is:

其中，测量矩阵大小为p×n²，测量矩阵的行代表一次测量中CCD探测器获取的所有像素点光强度值，列代表某一个像素点在p次测量中的获得的p个测量光强度值,所对应的p个桶探测值

作为压缩感知重建中的测量向量。Among them, the size of the measurement matrix is p×n ² , the rows of the measurement matrix represent the light intensity values of all pixels obtained by the CCD detector in one measurement, and the columns represent the p measured light intensities obtained by a certain pixel point in p measurements value, the corresponding p bucket detection values

as a measurement vector in compressed sensing reconstruction.

在某一稀疏变换域下，由测量向量和测量矩阵来恢复目标物体的方法，可通过求解最小l₁-范数下的最优化问题解决。于是CCPMGI方法中正图像可以由公式(10)求得：Under a certain sparse transformation domain, the method of recovering the target object from the measurement vector and measurement matrix can be solved by solving the optimization problem under the minimum l ₁ -norm. Therefore, the positive image in the CCPMGI method can be obtained by formula (10):

g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ⁺＝∫T(x,y)I_j ⁺(x,y)dxdy， (10)g ⁽²⁾ ∝T(x,y):argmin‖ΨT(x,y)‖ ₁ stD _j ⁺ =∫T(x,y)I _j ⁺ (x,y)dxdy, (10)

其中，‖·‖₁代表1-范数，Ψ为稀疏基。Among them, ‖· _‖1 represents the 1-norm, and Ψ is the sparse basis.

一种基于压缩感知的条件部分测量赝热光源关联成像方法，该方法包括以下步骤：A conditional partial measurement pseudothermal light source correlation imaging method based on compressed sensing, the method comprises the following steps:

步骤一：建立如图1所示的基于压缩感知的条件部分测量赝热光源关联成像方法；利用关联成像装置分别在物臂和参考臂进行M次测量，其中M<N,N＝n×n为目标物体的大小；物臂测量值被分成两部分，其中高于

的部分，记为

低于<D>的部分记为

对应地，将参考臂测量值即光场强度I_j(x,y)也分为{I_j ⁺(x,y)}和{I_j ^-(x,y)}两组测量矢量；Step 1: Establish a conditional partial measurement pseudothermal light source correlative imaging method based on compressed sensing as shown in Figure 1; use the correlative imaging device to perform M measurements on the object arm and the reference arm respectively, where M<N, N=n×n is the size of the target object; the object arm measurement is divided into two parts, which is higher than

part, denoted as

Parts below <D> are recorded as

Correspondingly, the measured value of the reference arm, that is, the light field intensity I _j (x, y) is also divided into two groups of measurement vectors: {I _j ⁺ (x, y)} and {I _j ^- (x, y)};

步骤二：将目标物体在稀疏基下稀疏化；对于图像目标物体，可采用离散余弦基或小波变换基等稀疏基；Step 2: Sparse the target object under the sparse basis; for image target objects, sparse bases such as discrete cosine bases or wavelet transform bases can be used;

步骤三：构造压缩感知重建算法的测量矩阵；取p个I_j ⁺(x,y)的光强度构造压缩感知重建方法的测量矩阵，其中

将每次光场分布

按行展开成一n²的行向量，p次测量结果依次排列构造出p×n²的测量矩阵Step 3: Construct the measurement matrix of the compressed sensing reconstruction algorithm; take p light intensities of I _j ⁺ (x, y) to construct the measurement matrix of the compressed sensing reconstruction method, where

Distribute each light field

Expand by row into a row vector of n ² , and arrange p times of measurement results in order to construct a measurement matrix of p×n ²

其中矩阵行代表一次测量中CCD探测器获取的所有像素点光强度值，列代表某一像素点在p次测量中的获得的p个测量光强度值；The rows of the matrix represent the light intensity values of all pixels obtained by the CCD detector in one measurement, and the columns represent p measured light intensity values obtained by a certain pixel in p measurements;

步骤四：构造压缩感知重建算法的测量值矢量；取构造测量矩阵的所对应的p个桶探测值依次排列构成出压缩感知重建中的测量值向量；Step 4: Construct the measured value vector of the compressed sensing reconstruction algorithm; take p buckets corresponding to the constructed measurement matrix for detection The values are arranged in sequence to form a vector of measurement values in compressed sensing reconstruction;

步骤五：取构造测量矩阵的所对应的p个桶探测

值构成压缩感知重建中的测量值向量，利用压缩感知重建方法，获得目标物体的关联正图像，满足关系：Step 5: Take p buckets corresponding to the constructed measurement matrix to detect

The value constitutes the measurement value vector in the compressed sensing reconstruction, and the associated positive image of the target object is obtained by using the compressed sensing reconstruction method, satisfying the relationship:

g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ⁺＝∫T(x,y)I_j ⁺(x,y)dxdy，其中，‖·‖₁代表1-范数，Ψ为稀疏基；g ⁽²⁾ ∝T(x,y):argmin‖ΨT(x,y)‖ ₁ stD _j ⁺ =∫T(x,y)I _j ⁺ (x,y)dxdy, where ‖· _‖1 represents 1-norm, Ψ is a sparse basis;

步骤六：选取低于<D>的部分

与其对应的I_j ^-(x,y)，利用关系式g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ^-＝∫T(x,y)I_j ^-(x,y)dxdy，通过压缩感知重建方法恢复目标物体的关联负图像。Step 6: Select the part below <D>

For its corresponding I _j ^- (x,y), use the relation g ⁽²⁾ ∝T(x,y):argmin‖ΨT(x,y)‖ ₁ stD _j ^- ＝∫T(x,y)I _j ^- (x,y)dxdy, recovers the associated negative image of the target object by compressed sensing reconstruction methods.

由于物臂求算数平均值后，其均值近似处于各项的中心位置。在恢复正图像时，需选取高于<D>的一半。因此，相对于传统GI方法,CCPMGI方法中构成压缩感知方法的测量矩阵和测量矢量都将是传统GI的数据量的一半，这样将大大地减少关联成像的恢复时间；另一方面，相对于CPMGI方法，CCPMGI方法中采用压缩感知技术，在同等成像性能下其测量次数将会远远小于CPMGI方法中的测量次数，有效地减少关联成像的时间，且压缩感知技术还可有效地提高成像质量。After calculating the arithmetic mean value of the object arm, its mean value is approximately in the center of each item. When restoring the positive image, it is necessary to select half of the value higher than <D>. Therefore, compared with the traditional GI method, the measurement matrix and measurement vector of the compressed sensing method in the CCPMGI method will be half of the data volume of the traditional GI method, which will greatly reduce the recovery time of correlation imaging; on the other hand, compared to the CPMGI Method, CCPMGI method uses compressed sensing technology, under the same imaging performance, the number of measurements will be much smaller than that of CPMGI method, effectively reducing the time of associated imaging, and compressed sensing technology can also effectively improve imaging quality.

有益效果：Beneficial effect:

1、本发明具有压缩感知重建方法的优点，并且结合了条件部分测量方法的特点。1. The present invention has the advantages of the compressed sensing reconstruction method, and combines the characteristics of the conditional part measurement method.

2、本发明在提高成像质量的同时，减少了在参考臂恢复物体像信息的测量次数，降低了成像的时间。2. While improving the imaging quality, the present invention reduces the number of measurements for recovering object image information on the reference arm, and reduces the imaging time.

附图说明Description of drawings

图1为本发明基于压缩感知的条件部分测量关联成像方法实现示意图。Fig. 1 is a schematic diagram of the implementation of the conditional partial measurement correlation imaging method based on compressed sensing in the present invention.

图2为本发明二灰度“中”物体的GI、CPMGI和CCPMGI数值仿真。Fig. 2 is the numerical simulation of GI, CPMGI and CCPMGI of the two-grayscale "medium" object of the present invention.

图3为本发明多灰度“boat”图的GI、CPMI和CCPMGI数值仿真图。Fig. 3 is a numerical simulation diagram of GI, CPMI and CCPMGI of the multi-grayscale "boat" diagram of the present invention.

图4为本发明GI、CPMI和CCPMGI三种关联成像方法中MSE随观测次数的变化曲线图。Fig. 4 is a graph showing the change of MSE with the number of observations in the three correlation imaging methods of GI, CPMI and CCPMGI of the present invention.

具体实施方式Detailed ways

以下结合说明书附图对本发明专利作进一步的详细说明。Below in conjunction with accompanying drawing, the patent of the present invention is described in further detail.

本发明为了验证本发明所提出的基于压缩感知的条件部分测量关联成像方法，现通过数值仿真进行验证。本仿真使用的赝热光源的波长为λ＝633nm高斯光。为了更客观准确地说明CCPMGI成像方法的性能，本发明引入均方误差参数(mean square error，MSE)，它表示恢复图像与目标物体的偏离程度。对于大小为M×N的目标物体，MSE定义为：In order to verify the conditional partial measurement correlation imaging method based on compressed sensing proposed by the present invention, the verification is now carried out through numerical simulation. The wavelength of the pseudothermal light source used in this simulation is λ=633nm Gaussian light. In order to describe the performance of the CCPMGI imaging method more objectively and accurately, the present invention introduces a mean square error parameter (mean square error, MSE), which represents the degree of deviation between the restored image and the target object. For a target object of size M×N, MSE is defined as:

$MSE MSE (({X x}_{i i,, j j},, {X x}_{i i,, j j}^{' '})) = = \frac{\underset{00 \leq \leq i i < < M m}{Σ Σ} \underset{00 \leq \leq j j < < N N}{Σ Σ} {(({X x}_{i i,, j j} - - {X x}_{i i,, j j}^{' '}))}^{22}}{M m \times \times N N} - - - - - - ((1111))$

其中，X_i,j和

分别代表原始物体和恢复图像。在此基础上，可以进一步定义重建图像的峰值信噪比(peak signal-to-noise rate,PSNR)，其中PSNR定义为Among them, Xi _,j and

represent the original object and the restored image, respectively. On this basis, the peak signal-to-noise ratio (PSNR) of the reconstructed image can be further defined, where PSNR is defined as

$PSNR PSNR (({X x}_{i i,, j j},, {X x}_{i i,, j j}^{' '})) = = 1010 lg lg [[\frac{{Val Val}_{max max}^{22}}{MSE MSE (({X x}_{i i,, j j},, {X x}_{i i,, j j}^{' '}))}]] - - - - - - ((1212))$

其中，

代表原始物体的灰度最大值。in,

Represents the maximum gray value of the original object.

如图1所示，本发明提供一种基于压缩感知的条件部分测量赝热光源关联成像方法，该方法是以赝热光源关联成像为基础，是以参考臂中成像的恢复仅与参考臂多次测量随机光场分布相关为前提，所述方法包括：1)物臂测量值被分成两部分，其中高于

的部分，记为

低于<D>的部分记为对应地，将参考臂测量值即光场强度I_j(x,y)也分为I_j ⁺(x,y)和I_j ^-(x,y)；考虑到目标图像物体的尺寸为64×64像素的图像物体，CCPMGI方法的测量次数设为2500，其中用于压缩感知重建的测量次数值为1250。2）将目标物体，如“中”或“boat”图，在离散余弦变换（discrete cosine transform,DCT）稀疏基下稀疏化；As shown in Figure 1, the present invention provides a conditional partial measurement pseudothermal light source correlation imaging method based on compressed sensing. Based on the premise that the random light field distribution of the secondary measurement is correlated, the method includes: 1) the measured value of the object arm is divided into two parts, wherein the value higher than

part, denoted as

Parts below <D> are recorded as Correspondingly, the light field intensity I _j (x, y) measured by the reference arm is also divided into I _j ⁺ (x, y) and I _j ^- (x, y); considering that the size of the target image object is 64× For a 64-pixel image object, the number of measurements of the CCPMGI method is set to 2500, and the number of measurements used for compressed sensing reconstruction is 1250. 2) The target object, such as the "middle" or "boat" image, is transformed into a discrete cosine transform (discrete cosine transform, DCT) sparse base sparse;

3）通过数值处理，获得CCPMGI方法中所需的{I_j ⁺(x,y)}和{I_j ^-(x,y)}等数据；3) Through numerical processing, obtain the required in the CCPMGI method Data such as {I _j ⁺ (x,y)} and {I _j ^- (x,y)};

4）取p个I_j ⁺(x,y)的光强度构造压缩感知重建方法的测量矩阵，其中

将每次光场分布

按行展开成一维行向量，得到1250×64²压缩感知测量矩阵为：4) Take p light intensities of I _j ⁺ (x, y) to construct the measurement matrix of the compressive sensing reconstruction method, where

Distribute each light field

Expanded into a one-dimensional row vector by row, the 1250×64 ² compressed sensing measurement matrix is obtained as:

其中测量矩阵行代表一次测量中CCD探测器获取的所有像素点光强度值，列代表某一像素点在p次测量中的获得的p个测量光强度值；

The rows of the measurement matrix represent the light intensity values of all pixels obtained by the CCD detector in one measurement, and the columns represent p measured light intensity values obtained by a certain pixel point in p measurements;

5）取构造测量矩阵的所对应的p＝1250个桶探测

值构成压缩感知重建中的测量值向量，利用正交匹配追踪(orthogonal matching pursuit，OMP)压缩感知恢复重建方法，获得目标物体的关联正图像，满足关系：g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ⁺＝∫T(x,y)I_j ⁺(x,y)dxdy，其中，‖·‖₁代表1-范数，Ψ为稀疏基；5) Take p=1250 buckets corresponding to the constructed measurement matrix to detect

The value constitutes the measured value vector in the compressed sensing reconstruction, using the orthogonal matching pursuit (OMP) compressed sensing recovery reconstruction method to obtain the associated positive image of the target object, satisfying the relationship: g ⁽²⁾ ∝T(x,y ):argmin‖∥T(x,y)‖ ₁ stD _j ⁺ =∫T(x,y)I _j ⁺ (x,y)dxdy, where,‖· _‖1 represents the 1-norm, and Ψ is the sparse basis;

6）同样，选取低于<D>的部分

与其对应的I_j ^-(x,y)，利用关系式g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ^-＝∫T(x,y)I_j ^-(x,y)dxdy，通过OMP压缩感知重建方法恢复目标物体的关联负图像。6) Similarly, select the part below <D>

For its corresponding I _j ^- (x,y), use the relation g ⁽²⁾ ∝T(x,y):argmin‖ΨT(x,y)‖ ₁ stD _j ^- ＝∫T(x,y)I _j ^- (x,y)dxdy, the associated negative image of the target object is recovered by the OMP compressed sensing reconstruction method.

为了说明CCPMGI方法相对于传统GI、CPMGI方法的优势，在相类似的实验原理图下分别对GI、CPMGI关联成像方法进行了数值仿真。针对“中”字和“boat”图两种不同灰度目标物体，在物臂和参考臂同时进行5000测量数据情形下，获得GI、CPMGI关联成像方法的成像结果。In order to illustrate the advantages of the CCPMGI method over the traditional GI and CPMGI methods, numerical simulations were carried out on the GI and CPMGI correlation imaging methods under similar experimental schematic diagrams. For two different grayscale target objects in the "中" character and "boat" image, the imaging results of the GI and CPMGI correlation imaging methods are obtained under the condition that the object arm and the reference arm carry out 5000 measurement data at the same time.

图2是针对二灰度“中”字符物体的成像结果，图3是针对8灰度“boat”图物体的成像结果。本发明研究结果表明，无论是二灰度图还是多灰度图，CCPMGI方法的成像质量要明显好于GI与CPMGI方法；而且CCPMGI方法的测量次数是GI与CPMGI方法的一半，成像恢复时压缩感知重建算法的测量次数是传统GI的1/4,CPMGI方法的1/2，这将大大地缩减了成像时间。Fig. 2 is the imaging result for the two-grayscale "medium" character object, and Fig. 3 is the imaging result for the 8-grayscale "boat" image object. The research results of the present invention show that no matter it is a two-grayscale image or a multi-grayscale image, the imaging quality of the CCPMGI method is obviously better than that of the GI and CPMGI methods; The number of measurements of the perceptual reconstruction algorithm is 1/4 of the traditional GI method and 1/2 of the CPMGI method, which will greatly reduce the imaging time.

本发明为了定量地对三种关联成像方法所获成像质量性能进行比较，现分别计算了三种关联成像方法下的均方误差MSE值和峰值信噪比值。由于赝热光源强度具有随机性，MSE和PSNR值是10次等同条件下成像结果的MSE和PSNR计算平均结果。表1是“中”字物体和“boat”图物体测量次数为5000次时的三种关联成像方法的均方误差MSE值和峰值信噪比PSNR值；表2则是针对以上两种物体测量次数为2500次时三种关联成像方法的均方误差值和峰值信噪比值。由此可见，无论是二灰度还是多灰度目标物体，基于压缩感知的条件部分测量关联成像方法所获得MSE值要明显小于其他两种方法；而且测量次数越大时，成像信息的MSE值较小，恢复物体的PSNR值越高。In order to quantitatively compare the imaging quality performance obtained by the three correlation imaging methods, the present invention now calculates the mean square error MSE value and the peak signal-to-noise ratio value under the three correlation imaging methods. Due to the randomness of the intensity of the pseudothermal light source, the MSE and PSNR values are the average results of MSE and PSNR calculations of 10 imaging results under the same conditions. Table 1 shows the mean square error MSE value and peak signal-to-noise ratio PSNR value of the three associated imaging methods when the number of measurements of the "中" character object and the "boat" image object is 5000 times; Table 2 is for the measurement of the above two objects The mean square error value and peak signal-to-noise ratio value of the three correlation imaging methods when the number of times is 2500. It can be seen that, whether it is a two-gray or multi-gray target object, the MSE value obtained by the conditional partial measurement correlation imaging method based on compressed sensing is significantly smaller than the other two methods; and when the number of measurements increases, the MSE value of the imaging information The smaller the value, the higher the PSNR value of the recovered object.

表1“中”字物体和“boat”图物体5000次时三种关联成像方法的均方误差MSE值和峰值信噪比值Table 1 The mean square error (MSE) value and peak signal-to-noise ratio (PSNR) value of the three correlation imaging methods when the "中" word object and the "boat" image object are 5000 times

MSEMSE “中”字"中" character Boat图Boat diagram GIGI 0.073710.07371 0.086760.08676 CPMGICPMGI 0.054410.05441 0.065990.06599 CCPMGICCPMGI 0.036930.03693 0.038260.03826 PSNRPSNR “中”字"中" character Boat图Boat diagram GIGI 11.324711.3247 10.616810.6168 CPMGICPMGI 12.643212.6432 11.805111.8051 CCPMGICCPMGI 14.326214.3262 14.171614.1716

表2“中”字物体和“boat”图物体2500次时三种关联成像方法的均方误差MSE值和峰值信噪比值Table 2 The mean square error (MSE) value and peak signal-to-noise ratio (PSNR) value of the three correlation imaging methods when the "中" character object and the "boat" image object are 2500 times

MSEMSE “中”字"中" character Boat图Boat diagram GIGI 0.092710.09271 0.096530.09653

CPMGICPMGI 0.065900.06590 0.075780.07578 CCPMGICCPMGI 0.047350.04735 0.051030.05103 PSNRPSNR “中”字"中" character Boat图Boat diagram GIGI 10.328710.3287 10.153410.1534 CPMGICPMGI 11.811111.8111 11.204311.2043 CCPMGICCPMGI 13.246813.2468 12.921712.9217

为了进一步比较三种成像方法的成像性能，本发明给出不同测量次数下“双缝”物体的三个成像方法的MSE值与测量次数的关系曲线，结果如图4所示。研究结果表明，与传统关联成像方法（GI）和基于部分测量关联成像方法(CMPGI)相比，在不同测量次数的条件下CCMPGI方法的MSE值都有明显改善。当测量次数为1500时，MSE值可趋向稳定，这是目标物体64*64=4096的Nyquist极限的36%；相同测量次数下，本方法计算得到MSE值仅是传统GI方法的一半左右，甚至更少，表明成像质量有了较大的改善，PSNR有明显的增长。In order to further compare the imaging performance of the three imaging methods, the present invention provides the relationship curves between the MSE value and the number of measurements of the three imaging methods of the "double slit" object under different measurement times, and the results are shown in Figure 4. The research results show that, compared with the traditional correlation imaging method (GI) and the partial measurement correlation imaging method (CMPGI), the MSE value of the CCMPGI method is significantly improved under the conditions of different measurement times. When the number of measurements is 1500, the MSE value tends to be stable, which is 36% of the Nyquist limit of the target object 64*64=4096; under the same number of measurements, the MSE value calculated by this method is only about half of the traditional GI method, or even Less, indicating that the imaging quality has been greatly improved, and the PSNR has increased significantly.

Claims

1. A method for measuring pseudothermal light source correlation imaging based on condition part of compressed sensing is characterized by comprising the following steps:

the method comprises the following steps: the arm measurement is divided into two parts, of which higher than

Section of

Is lower than<D>Is described asCorrespondingly, the reference arm measurement value, i.e. the light field intensity I_j(x, y) is also classified as I_j ⁺(x, y) and I_j ^-(x,y)；

Step two: the target object is thinned under a sparse basis, and for the image target object, the sparse basis can adopt a discrete cosine basis and a wavelet transform basis;

step three: performing M measurements on the object arm and the reference arm respectively by using associated imaging devices, wherein M is<N, N is the size of the target object, and the corresponding value is obtained

{I_j ⁺(x, y) } and { I_j ^-(x,y)}；

Step four: take p { I_j ⁺(x, y) } light intensity constructs the measurement matrix of the compressed sensing reconstruction method, where

Each time the light field is distributed

Spread into one-dimensional row vectors by row to obtain p × n²The compressed sensing measurement matrix is:

the row of the measurement matrix represents the light intensity values of all pixel points acquired by the CCD detector in one measurement, and the column represents p measurement light intensity values acquired by a certain pixel point in p measurements;

and 5: taking the corresponding p buckets that construct the measurement matrix for detection

The values form a vector of measured values in compressed sensing reconstruction, and the reconstruction method is recovered by using the compressed sensingThe method obtains the associated positive image of the target object, and satisfies the relation: g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ⁺＝∫T(x,y)I_j ⁺(x, y) dxdy, wherein |₁Represents 1-norm, psi is sparse base;

step 6: is selected to be lower than<D>Part (A) of

Corresponding to it I_j ^-(x, y) by the relation g⁽²⁾∝T(x,y):argmin‖ΨT(x,y)‖₁s.t.D_j ^-＝∫T(x,y)I_j ^-(x, y) dxdy, recovering the associated negative image of the target object by a compressed sensing reconstruction method.

2. The method for imaging by correlating the pseudo-thermal light source based on the conditional part measurement of the compressed sensing according to claim 1, wherein: the method is based on pseudo-thermal light source correlation imaging; the method is based on the premise that the recovery of the reference arm imaging is only equal to the random light field distribution measured by the reference arm for multiple times.

3. The method for imaging by correlating the pseudo-thermal light source based on the conditional part measurement of the compressed sensing according to claim 1, wherein: the method adopts a compressed sensing method.