CN103558606A - Condition part measuring associated imaging method based on compressive sensing - Google Patents
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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
Technical Field
The invention relates to a method for realizing a correlation imaging method based on compressed sensing, and belongs to the technical field of communication signal processing and quantum optical crossing.
Background
The associated imaging, also called Ghost Imaging (GI), is a novel imaging mode developed gradually in the nineteenth decades of the twentieth century, can provide a method for obtaining a clear image by using a conventional means, can solve the problem that some conventional imaging technologies are not easy to solve, can be applied to various fields such as satellite remote sensing, laser radar, medical imaging, military, industrial imaging and deep space exploration, and has a wide application prospect. When the traditional associated imaging is realized, the problems of more sampling times, long imaging time, imaging quality to be improved and the like exist. The novel associated imaging method which can reduce the imaging time of associated imaging and improve the quality of associated imaging is obtained, and is the premise that the associated imaging can be put into practical use.
In 2012, on the basis of pseudo-thermo-optic correlation imaging, roche et al proposed a correlation imaging method (CPMGI for short) based on conditional partial measurement. The method takes the measured value of the object arm as a judgment condition, and completely recovers the image of the target object by using only partial measured data of the reference arm. It gives a new idea that the image information of the associated imaging can be obtained by linear superposition of the measured values of the reference arm. However, although the recovery of image information in the conditional part measurement method has a reduced number of measurements compared with the common associated imaging method, the method still faces the problems of large data volume, long reconstruction time, more required physical storage and the like. On the other hand, the related imaging based on the compressed sensing can greatly reduce the sampling times, shorten the imaging time and improve the imaging quality. Therefore, the invention combines the Compressive sensing theory (CS) with the conditional partial measurement-based associated Imaging method, and provides a conditional partial measurement associated Imaging method (CCPMGI) based on Compressive sensing, so as to further reduce the measurement times of the Imaging recovery method, reduce the Imaging recovery time, and improve the Imaging quality, thereby having important theoretical significance and application value.
Disclosure of Invention
The invention aims to provide a method for realizing condition partial measurement correlation imaging based on compressed sensing, which adopts a partial condition measurement method, the sampling data of the method is equal to half of the sampling data of the traditional correlation imaging method, and the method can simultaneously give out a positive image and a negative image; meanwhile, the method further adopts an advanced signal processing method (a compressed sensing method) to reconstruct the image information of the object, and can obtain the image information of the object by using a convex optimal solution method with less measurement data. Therefore, the invention provides a reference method for the practicability of the correlation imaging.
The technical scheme is as follows:
the technical scheme adopted by the invention for solving the technical problems is as follows: a schematic diagram of the condition partial measurement pseudo-thermal light source correlation imaging method based on compressed sensing is shown in FIG. 1, and an optical distance between a barrel detector D and a pseudo-thermal light source is assumed to be Z1The optical distance between the CCD detector and the light source is Z2And assume Z1＝Z2. The emergent light of the pseudo-thermal light source passes through 50: after the 50 beam splitters, the light is divided into two independent light paths. One optical path is defined as the reference arm, whose beam propagates in free space to the CCD detector. The detection value of each CCD is marked as Ij(x, y), wherein j is 1,2<I(x,y)>Is defined as
The average value of the reference arm CCD detector after M times of measurement is obtained; the other optical path is defined as an object arm, after the light beam penetrates through the object with spatial distribution T (x, y), the light beam is received by a barrel detector D arranged behind the object arm, and the detection value of each barrel detector D is marked as DjWherein j is 1, 2.. times, M, and the average is obtained<D>Is defined as
Each detection value D of the bucket detector DjAre both related to the object transmission function T (x, y), i.e.:
Dj＝∫T(x,y)Ij(x,y)dxdy,j＝1,…,M, (1)
the associated imaging second order association function based on the pseudo thermal light source can be expressed as:
G(2)(x,y)＝G0+|∫T(x′,y′)δxx′δyy′dx′dy′|2， (2)
wherein G is0Is a constant whose normalized second order correlation function is:
g(2)(x,y)＝1+|∫T(x′,y′)δxx′δyy′dx′dy′|2， (3)
if the object arm and the reference arm are measured M times respectively, the normalized object arm and the normalized reference arm are cross-correlated into
Thus, the information of the object can be represented as
That is to say that the first and second electrodes,
therefore, the image information of the object obtained in the reference arm in the second-order correlation imaging of the pseudo-thermal light source can be detected by the reference arm to obtain the value Ij(x, y) and the object arm detection value DjIs obtained by weighted linear superposition. Due to the fact that<D>、<I(x,y)>Is a constant for the associated imaging process, so the object image information is divided into positive and negative image information and can be approximately expressed as
Wherein,
from this, mean of arm measurements<D>The threshold decision function is realized in the process of obtaining the object image information in the reference arm. In N<In the case of M times of measurement, the positive and negative dependence of object image information
The symbol of (2). If the arm measurement is divided into two parts, i.e. higher than<D>Section of
Is lower than<D>Section of
Correspondingly, the reference arm measurement value, i.e. the light field intensity I, is also usedj(x, y) is divided into Ij +(x, y) and Ij -(x, y); the positive image is composed of all Ij +Linear superposition of (x, y) } to obtain object image information; the negative image is composed of all { Ij -And (x, y) } linearly superimposing the obtained object image information. Intuitively, the reconstruction process of the positive and negative images is independent of the object being reconstructed, and relies only on the positive and negative distribution of the light field in the reference arm. Thus, if the size of the object is n × n, then at least M =1/2 × n × n different intensity distribution patterns in the reference arm are required to obtain positive and negative images of the object.
However, objects are usually sparse, i.e. they have only a small amount of spatial distribution not zero under a certain transform base representation, such as pictures with strong sparsity under a two-Dimensional discrete cosine transform (2D-DCT) or Wavelet Transform (WT). Therefore, positive and negative images of the conditional part measurement pseudo-thermal light source correlation imaging method can be obtained through a compressed sensing reconstruction method. The key point of the compressed sensing reconstruction method is to obtain related measurement vectors and measurement matrixes, and the measurement matrixes and sparse bases are required to be mutually uncorrelated.
Pseudo-thermal light source correlation imaging requires that the light field distribution has randomness, which satisfies the irrelevance 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 propagation cross-section of the light beam in the reference arm, x, y is 1, …, n, the light intensity distribution function at the j-th measurement of the M measurements is Ij(x, y), j 1.. times.m, in the form of a matrix:
wherein
The light field distribution size of a point (x, y) on the light beam propagation cross section, wherein x, y is 1, …, n. Matrix IjThe size is n × n, and if it is expanded into a one-dimensional row vector by rows, it can be obtained
After M measurements, p I are takenj +(x, y) light intensity as a measure matrix for a compressed sensing recovery method, wherein
The compressed sensing measurement matrix is:
wherein the measurement matrix size is p × n2The row of the measurement matrix represents the light intensity values of all pixel points acquired by the CCD detector in one measurement, the column represents p measurement light intensity values acquired by a certain pixel point in p measurements, and the corresponding p bucket detection values
As a measurement vector in compressed perceptual reconstruction.
Under a certain sparse transform domain, the method for recovering the target object by the measurement vector and the measurement matrix can solve the minimum l1-optimization problem solving under norm. The positive image in the CCPMGI method can then be obtained from equation (10):
g(2)∝T(x,y):argmin‖ΨT(x,y)‖1s.t.Dj +＝∫T(x,y)Ij +(x,y)dxdy， (10)
wherein |1Represents a 1-norm, and psi is a sparse base.
A method for measuring pseudothermal light source correlation imaging based on conditional part of compressed sensing comprises the following steps:
the method comprises the following steps: establishing a condition part measurement pseudo-thermal light source correlation imaging method based on compressed sensing as shown in FIG. 1; performing M measurements on the object arm and the reference arm respectively by using associated imaging devices, wherein M is<N, N × N is the size of the target object; the arm measurement is divided into two parts, of which higher than
Section of
Is lower than<D>Is described as
Correspondingly, the reference arm measurement value, i.e. the light field intensity Ij(x, y) is also classified as { Ij +(x, y) } and { Ij -(x, y) } two sets of measurement vectors;
step two: sparsifying the target object under a sparse basis; for the image target object, sparse bases such as a discrete cosine base or a wavelet transform base can be adopted;
step three: constructing a measurement matrix of a compressed sensing reconstruction algorithm; taking p Ij +(x, y) light intensity construction of a measurement matrix for a compressed sensing reconstruction method, wherein
Each time the light field is distributed
Spread into n by line2The p measurement results are sequentially arranged to construct p × n2Of the measurement matrix
The matrix row 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;
step four: constructing a measurement value vector of a compressed sensing reconstruction algorithm; taking the corresponding p buckets that construct the measurement matrix for detectionThe values are sequentially arranged to form a measured value vector in compressed sensing reconstruction;
step five: taking the corresponding p buckets that construct the measurement matrix for detection
The values form a measurement value vector in compressed sensing reconstruction, and a compressed sensing reconstruction method is utilized to obtain a correlation positive image of a target object, and the relationship is satisfied:
g(2)∝T(x,y):argmin‖ΨT(x,y)‖1s.t.Dj +＝∫T(x,y)Ij +(x, y) dxdy, wherein |1Represents 1-norm, psi is sparse base;
step six: is selected to be lower than<D>Part (A) of
Corresponding to it Ij -(x, y) by the relation g(2)∝T(x,y):argmin‖ΨT(x,y)‖1s.t.Dj -＝∫T(x,y)Ij -(x, y) dxdy, recovering the associated negative image of the target object by a compressed sensing reconstruction method.
After the object arm is subjected to arithmetic mean value, the mean value is approximately positioned at the center position of each item. In restoring a positive image, more than half of < D > needs to be chosen. Therefore, compared with the traditional GI method, the measurement matrix and the measurement vector which form the compressed sensing method in the CCPMGI method are half of the data volume of the traditional GI, so that the recovery time of the associated imaging is greatly reduced; on the other hand, compared with the CPMGI method, the CCMGI method adopts a compressed sensing technology, the measurement times of the CCMGI method are far less than those of the CPMGI method under the same imaging performance, the associated imaging time is effectively reduced, and the compressed sensing technology can also effectively improve the imaging quality.
Has the advantages that:
1. the method has the advantages of a compressed sensing reconstruction method and combines the characteristics of a condition part measuring method.
2. The invention improves the imaging quality, reduces the measurement times of restoring the object image information at the reference arm and reduces the imaging time.
Drawings
FIG. 1 is a schematic diagram of an implementation of a conditional partial measurement correlation imaging method based on compressive sensing according to the present invention.
FIG. 2 is a simulation of the GI, CPMGI, and CCPMGI values of a two-gray "medium" object of the present invention.
FIG. 3 is a simulation of the GI, CPMI, and CCPMGI values of a multi-gray "boat" diagram of the present invention.
FIG. 4 is a graph of MSE as a function of observation times for three correlating imaging methods of GI, CPMI, and CCPMGI of the present invention.
Detailed Description
The invention is further described in detail below with reference to the accompanying drawings.
In order to verify the condition partial measurement correlation imaging method based on compressed sensing, the invention carries out verification through numerical simulation. The wavelength of the pseudo-thermal light source used in the simulation is 633nm gauss. To more objectively and accurately illustrate the performance of CCPMGI imaging methods, the present invention introduces a mean square error parameter (MSE) that represents the degree of deviation of the restored image from the target object. For a target object of size M × N, MSE is defined as:
wherein, Xi,jAnd
representing the original object and the restored image, respectively. On the basis, a peak signal-to-noise ratio (PSNR) of the reconstructed image can be further defined, wherein the PSNR is defined as
Wherein,
representing the maximum value of the gray level of the original object.
As shown in fig. 1, the present invention provides a method for measuring pseudothermal light source correlation imaging based on conditional part of compressive sensing, which is based on pseudothermal light source correlation imaging and presupposes that the recovery of imaging in a reference arm is only related to the random light field distribution measured by the reference arm for many times, and the method includes: 1) 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 Ij(x, y) is also classified as Ij +(x, y) and Ij -(x, y); the number of measurements of the CCPMGI method is set to 2500 in consideration of an image object having a size of 64 × 64 pixels of a target image object, where the number of measurements for compressed sensing reconstruction is 1250. 2) Thinning the target object, such as a "middle" or "boat" graph, under a Discrete Cosine Transform (DCT) thinning basis;
3) by numerical processing, the values required in the CCPMGI method are obtained{Ij +(x, y) } and { Ij -(x, y) } and the like;
4) taking p Ij +(x, y) light intensity construction of a measurement matrix for a compressed sensing reconstruction method, wherein
Each time the light field is distributed
Spread into one-dimensional row vectors by row to obtain 1250 × 642The compressed sensing measurement matrix is:
5) taking the corresponding p-1250 buckets that make up the measurement matrix for probing
The values form a measurement value vector in compressed sensing reconstruction, and an Orthogonal Matching Pursuit (OMP) compressed sensing recovery reconstruction method is utilized to obtain a correlation positive image of a target object, and the relationship is satisfied: g(2)∝T(x,y):argmin‖ΨT(x,y)‖1s.t.Dj +＝∫T(x,y)Ij +(x, y) dxdy, wherein |1Represents 1-norm, psi is sparse base;
6) also, is selected to be lower than<D>Part (A) of
Corresponding to it Ij -(x, y) by the relation g(2)∝T(x,y):argmin‖ΨT(x,y)‖1s.t.Dj -＝∫T(x,y)Ij -(x, y) dxdy, recovering the associated negative image of the target object by an OMP compressed sensing reconstruction method.
In order to illustrate the advantages of the CCPMGI method compared with the traditional GI and CPMGI methods, numerical simulation was performed on the GI and CPMGI associated imaging methods respectively under similar experimental schematic diagrams. For two different gray scale target objects of the Chinese character 'Zhong' and the 'boat' images, under the condition that 5000 measurement data are simultaneously carried out on the object arm and the reference arm, the imaging results of the GI and CPMGI correlation imaging methods are obtained.
Fig. 2 is the imaging result for a two-gray "medium" character object, and fig. 3 is the imaging result for an 8-gray "boat" image object. The research result of the invention shows that the imaging quality of the CCPMGI method is obviously better than that of the GI and CPMGI methods no matter the two-gray-scale image or the multi-gray-scale image; moreover, the CCPMGI method has half the measurement times of the GI and CPMGI methods, and the compressed sensing reconstruction algorithm has 1/4 of the traditional GI and 1/2 of the CPMGI method when the imaging is recovered, so that the imaging time is greatly reduced.
In order to quantitatively compare the imaging quality performance obtained by the three correlation imaging methods, the mean square error MSE value and the peak signal-to-noise ratio under the three correlation imaging methods are calculated respectively. As the pseudo-thermal light source intensity has randomness, the MSE and PSNR values are the MSE and PSNR calculation average results of imaging results under 10 identical conditions. Table 1 shows mean square error MSE values and peak signal-to-noise ratio PSNR values of three correlation imaging methods when the number of times of measurement of the "medium" character object and the "boat" image object is 5000 times; table 2 shows the mean square error value and the peak signal-to-noise ratio of the three correlation imaging methods when the number of measurements on the two objects is 2500. Therefore, no matter the target object is a two-gray or multi-gray target object, the MSE value obtained by partially measuring the correlated imaging method based on the condition of compressed sensing is obviously smaller than that obtained by other two methods; and when the measurement times are larger, the MSE value of the imaging information is smaller, and the PSNR value of the recovered object is higher.
TABLE 1 mean square error MSE and Peak Signal-to-noise ratio of 5000 times of Chinese character object and Boat image object
| MSE | Chinese character' Zhong | Boat picture |
| GI | 0.07371 | 0.08676 |
| CPMGI | 0.05441 | 0.06599 |
| CCPMGI | 0.03693 | 0.03826 |
| PSNR | Chinese character' Zhong | Boat picture |
| GI | 11.3247 | 10.6168 |
| CPMGI | 12.6432 | 11.8051 |
| CCPMGI | 14.3262 | 14.1716 |
TABLE 2 mean square error MSE and Peak Signal-to-noise ratio values for 2500 times for the "Medium" and "Board" image objects
| MSE | Chinese character' Zhong | Boat picture |
| GI | 0.09271 | 0.09653 |
| CPMGI | 0.06590 | 0.07578 |
| CCPMGI | 0.04735 | 0.05103 |
| PSNR | Chinese character' Zhong | Boat picture |
| GI | 10.3287 | 10.1534 |
| CPMGI | 11.8111 | 11.2043 |
| CCPMGI | 13.2468 | 12.9217 |
In order to further compare the imaging performances of the three imaging methods, the invention provides a relation curve of MSE values and measurement times of the three imaging methods of the double-slit object under different measurement times, and the result is shown in FIG. 4. Research results show that compared with the traditional correlation imaging method (GI) and the correlation imaging method based on partial measurement (CMPGI), the MSE value of the CCMPGI method is obviously improved under the condition of different measurement times. When the number of measurements is 1500, the MSE value may tend to stabilize, which is 36% of the Nyquist limit for target object 64 x 64= 4096; under the same measurement times, the MSE value calculated by the method is only about half of that of the traditional GI method, and even less, which shows that the imaging quality is greatly improved, and the PSNR is obviously increased.
Claims (3)
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 Ij(x, y) is also classified as Ij +(x, y) and Ij -(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
{Ij +(x, y) } and { Ij -(x,y)}；
Step four: take p { Ij +(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.Dj +＝∫T(x,y)Ij +(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 Ij -(x, y) by the relation g(2)∝T(x,y):argmin‖ΨT(x,y)‖1s.t.Dj -＝∫T(x,y)Ij -(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.
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