CN110349233A - The single pixel dependent imaging that high quality is rebuild is realized using iterative phase searching algorithm - Google Patents
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Abstract
The present invention is a kind of single pixel dependent imaging for realizing that high quality is rebuild using iterative phase searching algorithm, step includes: 1) based on hadamard matrix, a series of intensity modes are pre-generated, each intensity mode is decomposed by a pair of noisy phase outline using iterative phase searching algorithm；2) collimated illumination is carried out to laser beam, each pair of phase section is sequentially embedded two pure phase spatial light modulators；It is carried out by the free-space propagation field of the first pure phase bit plane by using Fresel diffraction, the free-space propagation field by the second pure phase bit plane is also similar；The intensity of measurement is recorded by the bucket detector for not needing spatial resolution for being located at object rear；3) by the measurement intensity of record by with use that identical cascaded basis facility generates and a series of intensity modes calculated are interrelated；4) calculated referenced strength mode is associated with the intensity measured, and target is decrypted using correlation function.Method of the present invention is simple and easy to do.
Description
Technical field
The invention belongs to safety of image technical fields, are related to a kind of utilization iterative phase searching algorithm realization high quality reconstruction
Single pixel dependent imaging.
Background technique
Single pixel dependent imaging is also known as ghost imaging, is one of the optical technology of most attraction, because its brilliant physics is special
Property and receive more and more attention.Up to the present, the application based on single pixel imaging has been widely deployed.As optics is believed
The development of encryption for information technology, single pixel imaging technique the field application study more and more attention has been paid to.Most of all,
Through explored largely about single pixel imaging it is new configuration and algorithm, still, these algorithms not only need to reduce pendulous frequency with
Stringent hardware limitation, but also need to improve antimierophonic robustness and quick reconstruction image.
Summary of the invention
Realize that the single pixel that high quality is rebuild is related using iterative phase searching algorithm the object of the present invention is to provide a kind of
Imaging, the algorithm for solving the prior art not only needs to reduce pendulous frequency and stringent hardware limitation, but also needs to improve
The problem of antimierophonic robustness.
The technical scheme adopted by the invention is that a kind of single picture for realizing that high quality is rebuild using iterative phase searching algorithm
Plain dependent imaging, this method follow the steps below to implement:
Step 1: based on the hadamard matrix with certain order, having pre-generated a series of intensity modes, and used and change
Each intensity mode is decomposed into a pair of noisy phase outline for phase retrieval algorithm；
Step 2: in imaging process, collimated illumination being carried out to laser beam, each pair of phase section is sequentially embedded two pure phases
Bit space optical modulator；It is carried out, is passed through by using Fresel diffraction by the free-space propagation field of the first pure phase bit plane
The free-space propagation field of second pure phase bit plane is also similar；The intensity B of measurementiBy not needing sky positioned at object rear
Between resolution ratio bucket detector record；
Step 3: for reconstruction image, the measurement intensity of bucket detector record will give birth to identical cascaded basis facility is used
At and calculate a series of intensity modes it is interrelated；
Step 4: calculated referenced strength mode is associated with the intensity measured, is carried out using correlation function to target
Decryption.
Beneficial effects of the present invention include following aspect: 1) decryption effect is very satisfactory, is not using Gauss low pass
In the case where the post-processing such as filtering, picture material can be clearly observed.2) when the measurement intensity recorded with bucket detector is got over
Less, the lower image of visual quality can also be decrypted when reconstruction.3) it is directed to greyscale pattern, uses proposed single pixel related
Imaging system can also effectively obtain the decrypted result with high visual quality.4) Walsh-Hadamard mode be space just
It hands over, without any redundancy, reconstructed results are very clear, and the result than stochastic model decryption is much better.Actual measurement is reduced simultaneously
The quantity of intensity, substantially increases imaging efficiency.
Detailed description of the invention
Fig. 1 is the systematic schematic diagram for the single pixel dependent imaging that the present invention uses；
Fig. 2 a is the typical module generated from a row vector of Hadamard matrix, and Fig. 2 b is first phase profile, figure
2c is second phase profile, and Fig. 2 d is the graph of relation between the number of iterations and related coefficient；
Fig. 3 a is each pair of phase outline αi(x, y) and βiCorrelation between (ξ, η), Fig. 3 b are first in set α (x, y)
Correlation in set and set (ξ, η) between phase outline between all profiles, Fig. 3 c is first in set β (ξ, η)
The correlation between all profiles in phase outline and set (x, y).
Fig. 4 a is original binary image, and Fig. 4 b is the distribution of measurement intensity, and Fig. 4 c is the weight using second order related algorithm
It builds, Fig. 4 d is using l0Smoothing algorithm is optimized reconstruction；
Fig. 5 a, Fig. 5 b, Fig. 5 c, Fig. 5 d are to be surveyed using 30%, 50%, 70%, 90% phase outline to record respectively
The decryption of intensity；
Fig. 6 a be using 1.5% phase outline pair decoding pattern, Fig. 6 b is corresponding nonlinear correlation figure；
Fig. 7 a is grayscale image, and Fig. 7 b is using second order related algorithm reconstruction figure, and Fig. 7 c is the phase outline pair using 3.5%
Figure is rebuild, Fig. 7 d is corresponding nonlinear correlation figure.
In figure, 1. lasers, 2. lens, 3. spatial light modulators one, 4. spatial light modulators two, 5. objects, 6. barrels of spies
Survey device, 7. processors.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
In order to improve the quality with less measurement intensity reconstruction image, retrieved the invention proposes a kind of using iterative phase
Algorithm realizes the single pixel dependent imaging (method) that high quality is rebuild, and adopts as shown in Figure 1, the present invention carries out single pixel dependent imaging
Sensing infrastructure is cascaded with a kind of optics, structure setting is, including the laser 1, thoroughly set gradually along horizontal axis
Mirror 2, spatial light modulator 1, spatial light modulator 24, object 5, bucket detector 6 and processor 7.
The method of the present invention is followed the steps below to implement using above-mentioned optics cascade sensing infrastructure:
Step 1: based on the hadamard matrix with certain order, having pre-generated a series of intensity modes, and used and change
Each intensity mode is decomposed into a pair of noisy phase outline for phase retrieval algorithm, detailed process is:
Assuming that K is the sum of pattern, a series of intensity mode Ii(μ, ν) [i=1,2,3 ..., K] it is to pre-generate to have
The Hadamard matrix of certain order, and it is a pair of noisy to use iterative phase searching algorithm to be decomposed into each intensity mode
Phase outline αi(x, y) and βi(ξ, η), wherein (x, y) and (ξ, η) respectively indicates the plane in two stages of coordinate,
The basic block of 2 ranks is mathematically defined as commonly used in the hadamard matrix of building arbitrary order:
Then, being obtained using following recurrence formula has 2kHadamard matrix:
The Hadamard matrix of any sequence is all square and symmetrical, wherein each element is equal to+1 or -1；Assuming that
The size for the object to be imaged is M × N pixel, meets condition M × N=2k；Being calculated with formula (1) and formula (2) has rank
Number 2kHadamard matrix after, between row vector apply random permutation, and in each row vector with -1 member
Element is arranged to 0；Then, the i-th row vector is rearranged into two-dimensional intensity mode Ii(μ, ν) has M × N pixel；Therefore, it produces
Raw in total 2kA intensity pattern, during being completely or partially used for single pixel dependent imaging,
In order to obtain corresponding phase outline αi(x, y) and βi(ξ, η), using a kind of Phase Retrieve Algorithm of iteration, specifically
Process is as follows:
1.1) by two phase-only mask exp (j αi(x, y)) and exp (j βi(ξ, η)) M × N number of pixel is generated, wherein two
A initial phase profile random distribution in [0,2 π] range；In subsequent iterative step, by the way that intensity mode is considered as width
Degree constraint is to update these phase outlines；
1.2) in being taken turns n-th, the wave propagated forward between first phase plane and second phase plane, expression formula are as follows:
Wherein, d1Indicate the axial distance between two phase planes；
1.3) it is propagated forward between second phase plane and object plane, expression formula are as follows:
Wherein, d2Indicate the axial distance between second phase plane and object plane；
1.4) intensity mode I is appliedi(μ, ν) is that amplitude constrains to update complex value waveThen back-propagation,
Expression formula are as follows:
Wherein, FWPλ,-dIndicate free space backpropagation, | | indicate modulo operation；
1.5) in the case where obtaining wavefront and helping, phase-only mask is updatedIt is uniquely put down in second stage
On face, expression formula are as follows:
1.6) complex value wave is updatedThen wave back-propagating, expression formula are executed are as follows:
1.7) phase-only mask in first pure phase bit plane is updated, expression formula are as follows:
1.8) estimate the related coefficient CC between object amplitude,With pre-generated mode Ii(μ, ν) meter
Calculating is convergence, to determine whether iterative process stops, expression formula are as follows:
Wherein, E [] indicates that coordinate is omitted for brevity in desired value operator；In general, by very close 1 reality
Numerical value is set as the threshold value of related coefficient, to guarantee to realize best iteration result；
1.9) repeat the above steps 1.2)-step 1.8), until CC value reaches predetermined threshold；Once iterative process terminates
When, the result of final updatingWithIt will be considered as the phase outline of two decomposition.
Step 2: in imaging process, collimated illumination being carried out to laser beam, each pair of phase section is sequentially embedded two pure phases
Bit space optical modulator；It is carried out, is passed through by using Fresel diffraction by the free-space propagation field of the first pure phase bit plane
The free-space propagation field of second pure phase bit plane is also similar；The intensity B of measurementiBy not needing sky positioned at object rear
Between resolution ratio bucket detector record, detailed process is:
In imaging process, collimated illumination is carried out to laser beam, each pair of phase section is sequentially embedded two pure phase bit spaces
Optical modulator；Wave is by two phase-only mask exp (j αi(x, y)) and exp (j βi(ξ, η)),Obtained speckle pattern
Case passes through object；The intensity B of measurementiBy being located at the bucket detector record for not needing spatial resolution at object rear, mathematics
Expression formula are as follows:
Wherein, T (μ, ν) is the transmission function of object, and (μ, ν) is the transversal coordinate of objective plane, FWPλ,dIndicate freely empty
Between wave propagation, λ is optical wavelength, and d is axial distance；
It is carried out by the free-space propagation field of first phase plane using Fresel diffraction, expression formula are as follows:
Wherein, * indicates convolutional calculation, h (x, y, d1) be Fresnel propagation point impulse function, is defined as:
Similarly, pass through the free-space propagation field expression formula of second phase plane are as follows:
Corresponding impulse function indicates are as follows:
Step 3: for reconstruction image, the measurement intensity of bucket detector record will give birth to identical cascaded basis facility is used
At and calculate a series of intensity modes it is interrelated, detailed process is:
For reconstruction image, the measurement intensity recorded by bucket detector by with a series of intensity mode I for being expressed asi'(μ,
ν) [i=1,2,3 ..., K] is interrelated, is generated simultaneously using identical cascaded basis facility (optics cascade sensing infrastructure)
It is calculated as
Step 4: calculated referenced strength mode is associated with the intensity measured, is carried out using correlation function to target
Decryption, detailed process is:
Referenced strength mode Ii(μ, ν) and the intensity B measurediIt is associated, target is decrypted using correlation function,
The expression formula of the correlation function are as follows:
?.
Validity experiment is carried out to the present invention
To evaluate the validity of single pixel dependent imaging method of the invention as shown in figure 1, use wavelength for the flat of 632.8nm
Surface wave and 740.4 μm of simulation illuminations.When the intensity pattern generated in advance is resolved into two noisy phase outlines, it is axial away from
From d1And d2It is respectively set as 30mm and 44mm.In the intensity that record processing measures, a series of phase-only mask exp (j αi(x,
) and exp (j β y)i(ξ, η)) [i=1,2,3 ..., K] it cascades and is sequentially embedded to two with 64 × 64 pixel sizes and picture
20 μm of spatial light modulator of plain spacing.In order to prove, the set of α (x, y) is expressed as by first pure phase bit plane
The phase outline of retrieval forms, and set β (ξ, η) is made of the phase outline in second stage.
It is shown in fig. 2 a from order 212Hadamard matrix a row vector derive it is pre-generated
Intensity mode.It indicates that the size of each intensity pattern is 64 × 64 pixels.Show two phases respectively in Fig. 2 b and Fig. 2 c
The phase outline answered, they are extracted by using iterative phase searching algorithm.The phase retrieval process proposed has height
Convergence rate, and after executing 6 iteration, green strength mode and its estimate between correlation coefficient value reach 0.99
More than.
Intensity mode shown in a according to fig. 2, the relationship between the number of iterations and related coefficient are as shown in Figure 2 d.For it
His intensity mode, can obtain similar relation curve.In single pixel dependent imaging method, the phase wheel extracted preferably is avoided
It is wide that there is strong correlation each other.Fig. 3 a is each pair of phase outline αi(x, y) and βiCorrelation between (ξ, η), Fig. 3 b are collection
The correlation in the set in α (x, y) between first phase profile and set (ξ, η) between all profiles is closed, Fig. 3 c is set β
The correlation between all profiles in first phase profile and set (x, y) in (ξ, η).As can be seen from these figures,
The phase outline retrieved be it is very incoherent, this realizes the requirement of single pixel associated imaging system.
Fig. 4 a shows the binary picture of 64 × 64 pixels, will use proposed single pixel dependent imaging method
It is encrypted.When being sequentially embedded in all phase outline clock synchronizations, the 4096 measurement intensity groups recorded by bucket detector can be obtained
At a n dimensional vector n.Fig. 4 b depict measurement intensity as a result, it can be seen that the information of original binary image is complete
It encrypts and the distribution of measurement intensity is random.Other than all phase outlines pair, there are also optical parameter such as optical wavelength
Main key is considered with axial distance.When correctly applying all keys, second order related algorithm can be used to original
Beginning image is decrypted.As illustrated in fig. 4 c, it is evident that decrypted result is very satisfactory, wherein not using such as Gauss low pass
Structured content is clearly viewed in the case of the post-processing of filtering.In order to quantitatively assess the quality of reconstructed results, master pattern
Noise ratio (PSNR) is to calculate between its reconstruction image are as follows:
Wherein, f indicates that master pattern, g indicate reconstructed results.For brevity, coordinate is omitted.It is square between them
Error (MSE) indicates are as follows:
For rebuilding shown in Fig. 4 c, Y-PSNR and related coefficient are respectively 46.4176dB and 0.999955.It uses
Smooth l0The optimization methods such as algorithm can be further improved the quality of reconstructed results.With Hi-Fi optimized reconstruction such as Fig. 4 d
Shown, Y-PSNR is equal to 1, and related coefficient reaches 274.6880dB.
The present invention is verified
When with bucket detector record small number of measurement intensity for rebuild when, can also decrypt with lower vision matter
The pattern of amount.Therefore, the quantity that phase outline pair is reduced as far as under the premise of certain vision requirement is one important
The problem of, this will be convenient for management key.When 30.0%, 50.0%, 70.0% and 90.0% phase outline is to being cascaded and suitable
When the intensity that sequence is embedded into two spaces optical modulator to record measurement, the pattern of decryption is respectively displayed on Fig. 5 a, Fig. 5 b, figure
In 5c and Fig. 5 d, corresponding peak signal noise ratio, mean square error and related coefficient are listed in Table 1 below.
Table 1 be respectively using 30%, 50%, 70%, 90% phase outline reconstructed results PSNR, MSE and CC value
(table 1 has been added in attached drawing)；
Table 1, four kind of phase outline reconstructed results compare
As can be seen that the increase with phase outline to quantity, the quality for decrypting pattern is continuously improved.It is noticeable
It is, although the phase outline with 30.0% is very fuzzy to the image of reconstruction, it can be seen that the information of master pattern.This
Outside, if you do not need to visually observing master pattern, nonlinear correlation algorithm can be used to utilize very small amount of phase
Profile is to verifying its existence.Fig. 6 a show using only 1.5% phase outline pair decryption noise pattern, therefrom not
Any significant information can be obtained.But corresponding nonlinear correlation figure pattern and its rebuild between relationship show it is original
The presence of object, because only observing a spike in figure 6b.
For gray level image, use proposed single pixel associated imaging system that can also effectively obtain with high vision
The decrypted result of quality.As shown in Figure 7a, the pattern quilt with 64 × 64 pixels cut from the central part of image " Lena "
It is considered raw information, is selected from USC-SIPI image data base.By using second order related algorithm, from the intensity of all measurements
Decryption is rebuild, and is recorded with 4096 pairs of phase outlines, as shown in Figure 7b.Similar to shown in Fig. 4 c as a result, can complete area
Divide the structured content of master pattern.Y-PSNR and related coefficient are respectively 47.0479dB and 0.9998.It is shown in Fig. 7 c
When the reconstruction of the phase outline clock synchronization using only 3.5%, wherein not shown any significant information.Figure is depicted in Fig. 7 d
Case and its rebuild between nonlinear correlation figure, wherein only observing a significant peak value in noisy background to prove original object
The presence of body.It is worth noting that, the quantity for the phase outline pair applied in single pixel associated imaging system increases to centainly
Degree, because grayscale mode has bigger spectral range and more information compared with binary mode.
Irradiate object using Walsh-Hadamard mode to record the intensity pair of measurement, and by a pair of of measurement intensity it
Between difference be considered as result.Because Walsh-Hadamard mode is spatially orthogonal without any redundancy, weight
Build that result is very clear and the result than being decrypted with stochastic model is much better.Meanwhile reducing the quantity of measurement intensity, thus
Imaging efficiency can be greatly improved.Compared with the imaging scheme, the single pixel associated imaging system proposed has higher effect
Rate.The object of 64 × 64 pixels according to shown in Fig. 4 a is needed with the record of bucket detector 6 8192 in total in the above scheme
Measurement intensity, and 4096 measured values are only collected in imaging method proposed by the invention.
Claims (5)
1. a kind of single pixel dependent imaging for realizing that high quality is rebuild using iterative phase searching algorithm, which is characterized in that according to
Following steps are implemented:
Step 1: based on the hadamard matrix with certain order, having pre-generated a series of intensity modes, and used iteration phase
Each intensity mode is decomposed into a pair of noisy phase outline by position searching algorithm；
Step 2: in imaging process, collimated illumination being carried out to laser beam, it is empty that each pair of phase section is sequentially embedded two pure phase positions
Between optical modulator；It is carried out by the free-space propagation field of the first pure phase bit plane by using Fresel diffraction, passes through second
The free-space propagation field of pure phase bit plane is also similar；The intensity B of measurementiThe space that do not need by being located at object rear is divided
The bucket detector of resolution records；
Step 3: for reconstruction image, the measurement intensity of bucket detector record will generate simultaneously with identical cascaded basis facility is used
A series of intensity modes calculated are interrelated；
Step 4: calculated referenced strength mode is associated with the intensity measured, is solved using correlation function to target
It is close.
2. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm,
It is characterized in that, detailed process is in the step 1:
Assuming that K is the sum of pattern, a series of intensity mode Ii(μ, ν) [i=1,2,3 ..., K] it is pre-generated with certain
The Hadamard matrix of order, and each intensity mode is decomposed by a pair of noisy phase using iterative phase searching algorithm
Profile αi(x, y) and βi(ξ, η), wherein (x, y) and (ξ, η) respectively indicates the plane in two stages of coordinate,
The basic block of 2 ranks is mathematically defined as commonly used in the hadamard matrix of building arbitrary order:
Then, being obtained using following recurrence formula has 2kHadamard matrix:
The Hadamard matrix of any sequence is all square and symmetrical, wherein each element is equal to+1 or -1；Assuming that will be at
The size of the object of picture is M × N pixel, meets condition M × N=2k；Being calculated with formula (1) and formula (2) has order 2k's
After Hadamard matrix, random permutation is applied between row vector, and the element in each row vector with -1 is set
It is set to 0；Then, the i-th row vector is rearranged into two-dimensional intensity mode Ii(μ, ν) has M × N pixel；Therefore, it generates in total
2kA intensity pattern, during being completely or partially used for single pixel dependent imaging,
In order to obtain corresponding phase outline αi(x, y) and βi(ξ, η), using a kind of Phase Retrieve Algorithm of iteration, detailed process
It is as follows:
1.1) by two phase-only mask exp (j αi(x, y)) and exp (j βi(ξ, η)) M × N number of pixel is generated, at the beginning of two of them
Beginning phase outline random distribution in [0,2 π] range；In subsequent iterative step, by the way that intensity mode is considered as amplitude about
Beam updates these phase outlines；
1.2) in being taken turns n-th, the wave propagated forward between first phase plane and second phase plane, expression formula are as follows:
Wherein, d1Indicate the axial distance between two phase planes；
1.3) propagated forward between second phase plane and object plane, expression formula are as follows:
Wherein, d2Indicate the axial distance between second phase plane and object plane；
1.4) intensity mode I is appliedi(μ, ν) is that amplitude constrains to update complex value wave Vi (n)(μ, ν), then back-propagation, expression formula
Are as follows:
Wherein, FWPλ,-dIndicate free space backpropagation, | | indicate modulo operation；
1.5) in the case where obtaining wavefront and helping, phase-only mask is updatedIn the unique plane of second stage,
Expression formula are as follows:
1.6) complex value wave W is updatedi (n)(ξ, η) then executes wave back-propagating, expression formula are as follows:
1.7) phase-only mask in first pure phase bit plane is updated, expression formula are as follows:
1.8) estimate the related coefficient CC between object amplitude, | Vi (n)(μ,ν)|2With pre-generated mode Ii(μ, ν) is calculated as
Convergence, to determine whether iterative process stops, expression formula are as follows:
Wherein, E [] indicates desired value operator；Set very close 1 real number value to the threshold value of related coefficient；
1.9) repeat the above steps 1.2)-step 1.8), until CC value reaches predetermined threshold；Once at the end of iterative process, most
The result updated afterwardsWithIt will be considered as the phase outline of two decomposition.
3. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm,
It is characterized in that, detailed process is in the step 2:
In imaging process, collimated illumination is carried out to laser beam, each pair of phase section is sequentially embedded two pure phase bit space light tune
Device processed；Wave is by two phase-only mask exp (j αi(x, y)) and exp (j βi(ξ, η)),Obtained speckle pattern is worn
Cross object；The intensity B of measurementiBy being located at the bucket detector record for not needing spatial resolution at object rear, mathematical expression
Formula are as follows:
Wherein, T (μ, ν) is the transmission function of object, and (μ, ν) is the transversal coordinate of objective plane, FWPλ,dIndicate free space wave
Propagation, λ is optical wavelength, and d is axial distance；
It is carried out by the free-space propagation field of first phase plane using Fresel diffraction, expression formula are as follows:
Wherein, * indicates convolutional calculation, h (x, y, d1) be Fresnel propagation point impulse function, is defined as:
Similarly, pass through the free-space propagation field expression formula of second phase plane are as follows:
Corresponding impulse function indicates are as follows:
4. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm,
It is characterized in that, detailed process is in the step 3:
For reconstruction image, the measurement intensity recorded by bucket detector by with a series of intensity mode I ' for being expressed asi(μ,ν)[i
=1,2,3 ..., K] it is interrelated, it generates and is calculated as using identical cascaded basis facility
5. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm,
It is characterized in that, detailed process is in the step 4:
Referenced strength mode Ii(μ, ν) and the intensity B measurediIt is associated, target is decrypted using correlation function, the phase
Close the expression formula of function are as follows:
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| 张雷洪等: "在课堂上实现基于激光投影仪和哈达玛矩阵的关联成像研究", 《应用激光》 * |
| 武晓嘉等: "基于结构化观测矩阵的低复杂度视频编码", 《数据采集与处理》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113163201A (en) * | 2021-03-04 | 2021-07-23 | 北京理工大学 | Video multi-frame reconstruction method and device based on single-pixel camera |
| CN113163201B (en) * | 2021-03-04 | 2022-03-22 | 北京理工大学 | Video multi-frame reconstruction method and device based on single-pixel camera |
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| CN110349233B (en) | 2022-10-11 |
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