CN109115681A - A kind of sparse imaging system of steady quantum and method - Google Patents
A kind of sparse imaging system of steady quantum and method Download PDFInfo
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Abstract
The invention belongs to quantum imaging technical fields, it discloses a kind of sparse imaging system of steady quantum and method, the system includes: laser, half-wave plate, bbo crystal, the first condenser lens, beam splitter, the second condenser lens, spatial light modulator, the first single-photon detector, the second single-photon detector, Single Photon Counting card and computer.In the case where there is interference and systematic error, the present invention can guarantee the robustness of imaging.
Description
Technical field
The invention belongs to quantum imaging technical field, it is related to a kind of sparse imaging system of steady quantum and method, specifically
For, be it is a kind of based on tangle two-photon, to systematic error and the sparse imaging method of the steady quantum of interference and device, when depositing
In the case where interference and systematic error, it can guarantee the robustness of imaging.
Background technique
Quantum imaging is to make mutually independent signal space and ginseng using quantum entanglement as a kind of novel imaging technique
The object image information in one of space can be transmitted by examining space, thus also by quantum imaging be known as relevance imaging or ghost at
Picture.
In tradition imaging, be primarily present following three defects: 1) imaging resolution is limited by Rayleigh diffraction limit；2) at
Two-dimensional scanning data as needing to be received picture with surface detector；3) interference and noise easily have an impact imaging, tie imaging
Fruit resolution ratio is low.The appearance of quantum imaging technology compensates for these deficiencies, offers great advantages, in that 1) quantum imaging resolution ratio
It can break through Rayleigh limit, achieve the purpose that super-resolution；2) quantum imaging does not need to use planar detector, it is only necessary to two lists
Photon detector can complete detection, the case where suitable for not being available bulky planar detector, save cost；3) it measures
Target road and reference arm in sub- imaging device be separation, have certain anti-interference ability, using associate feature carry out at
As there is anti-interference advantage compared to traditional optical imaging.Therefore, quantum imaging is in military remote sensing, medical imaging and language
The fields such as sound transmission, wireless communication have broad application prospects.Simultaneously quantum imaging there is also defects, such as equipment costly,
Sampling meets the time is longer, data processing amount is larger etc..
Compressive sensing theory is a kind of completely new acquisition letter that D.Donoho, J.Romberg and E.Candes et al. are proposed
Number and image method, which proposes when handle signal, a certain transform domain can be transformed data to, this
Transform domain be it is sparse, can carry out data compression, break through the limitation of nyquist sampling law, recycle compressed sensing iteration
The signal in sparse domain is reconstructed in optimal reconfiguration algorithm, obtains required original signal imaging effect.Compressed sensing is managed
By applying in quantum imaging, preferable imaging effect can be obtained in the case where hits is few, effectively shorten imaging time.
In current quantum imaging compressive sensing theory, use under Spontaneous Parametric that conversion generates tangle two-photon as
Light source, and pass through the Random Graph of spatial light modulator (Spatial Light Modulator, SLM) load to reference arm light source
Case is modulated, then carries out coincidence counting with the light source on target road, and reconstruct obtains original image.It is typically chosen random matrix conduct
Observing matrix can not be stored since random matrix has uncertainty, and it is larger to lead to be imaged recovery effects gap every time, adopted
Recovery effects are bad in the case that sample number is few.In addition, systematic error and interference are inevitable in actual imaging process, it is
System error and interference can make the coincidence counting of existing method generate deviation, so that imaging effect be made to decline.
Summary of the invention
In view of the deficiency of the prior art, the present invention proposes a kind of sparse imaging system of steady quantum and side
Method can guarantee the robustness of imaging in the case where there is interference and systematic error.
To reach above method purpose, the present invention is realised by adopting the following technical scheme:
In a first aspect, providing a kind of sparse imaging system of steady quantum, comprising: laser, half-wave plate, bbo crystal,
One condenser lens, beam splitter, the second condenser lens, spatial light modulator, the first single-photon detector, the second single photon detection
Device, Single Photon Counting card and computer；
Wherein, the laser, for emitting laser to the half-wave plate；
The half-wave plate for receiving the laser of the laser transmitting, and generates polarised light, sends out to the bbo crystal
Penetrate the polarised light；
The bbo crystal carries out spontaneous ginseng to the polarised light for receiving the polarised light of the half-wave plate transmitting
It is converted to entangled light under amount, emits entangled light to first condenser lens；
First condenser lens, for focusing the entangled light of the first condenser lens transmitting to enhance entangled light
Light intensity, and then to the beam splitter emit by convergence entangled light；
The beam splitter, it is described through over-focusing entangled light for receiving, to the entangled light by convergence point
Horizontally light beam and vertical direction light beam two-way light beam；Wherein, directive waits for after vertical direction light beam projects the beam splitter
Imaging object, vertical direction light beam are denoted as target beam；Spatial light described in directive after the horizontal direction light beam injection beam splitter
Modulator, vertical direction light beam are denoted as reference beam；
First single-photon detector for receiving through the target beam after object to be imaged, and is detected and is wherein wrapped
The photon contained, and then detection photon is sent to the Single Photon Counting card；
Second condenser lens, for focusing the reference beam, so that the reference beam is radiated at spatial light tune
On device processed；
The spatial light modulator carries out width to the reference beam for loading gray scale picture, and using gray scale picture
Degree modulation obtains modulation light beam, and emits the modulation light beam to second single-photon detector；Wherein, the grayscale image
Piece is transformed according to pre-generated certainty random matrix；
Described second single-photon detector for receiving the modulation light beam, and detects photon wherein included, Jin Erxiang
The Single Photon Counting card sends detection photon；
The Single Photon Counting card is used for first single-photon detector and second single photon detection
The detection photon that device is sent, and coincidence counting is carried out to the two, corresponding coincidence counting value is obtained, and send institute to the computer
State coincidence counting value；
The computer, for receiving the coincidence counting value, and then according to the coincidence counting value and described pre- Mr.
At certainty random matrix the object to be imaged is imaged, obtains and shows image using quantum imaging model
Piece.
Second aspect provides a kind of sparse imaging method of steady quantum, comprising the following steps:
Step 1, M certainty random matrix is generated, and converts corresponding M for the M certainty random matrix
Gray scale picture；Wherein, the dimension of each certainty random matrix is N × N-dimensional, and N × N indicates that preset imaging resolution, N are positive
Integer, N > 1；
Step 2, the M gray scale picture is successively loaded onto spatial light modulator, so that spatial light modulator utilizes institute
It states M gray scale picture and amplitude modulation is carried out to the reference beam, obtain M amplitude different modulating light beam, and then make time phase
It closes single photon counting card and obtains M different coincidence counting values；
Step 3,1 × N is converted by each certainty random matrix2The row vector of dimension obtains M 1 × N2The row of dimension to
Amount, and using wherein each row vector as a line of matrix to get to a M × N2The matrix of dimension is denoted as calculation matrix A；It will
The M different coincidence counting values are write as a column vector, are denoted as measured value C；
Step 4, according to the calculation matrix A, the measured value C, quantum imaging model: C=(A+ Δ A) × T+ Δ is established
E；Wherein, T indicates that target column vector, the lattice point error and modulation error that Δ A representation space optical modulator occurs, Δ E indicate dry
It disturbs and systematic error；
Step 5, building and solving optimization problem:Obtain mesh
Mark the sparse transformation vector x of column vector T；According to the transformation of coefficient vector x and sparse basis Ψ, target column vector T=is obtained
Ψx；
Wherein, Ψ indicates sparse basis,Indicate cost function, λ | | x | |1For regularization term, λ indicates regularization
Coefficient, | | | |FIndicate Frobenius norm, | | | |1Indicate L1 norm
Step 6, the target column vector T is reduced to N × N-dimensional matrix to get the image of object to be imaged is arrived.
Based on the sparse imaging system of steady quantum provided by the invention and method, the laser that laser is issued is through filtering
Play on bbo crystal generation after wave and polarization adjustment polarization direction is mutually perpendicular and tangle two-photon pair, then passes through beam splitter
Light beam is divided into two-way, light beam shines in target all the way, referred to as target beam；Another way light beam is adjusted by spatial light modulator
System, referred to as reference beam.By single-photon detector by two-way photon collection, be transferred in Single Photon Counting card into
Row match operation obtains multiple coincidence counting values by changing observing matrix of the load in spatial modulator；It considers further that and is
Error of uniting and interference, model imaging formula again, obtain a kind of sparse steady calculation suitable under actual conditions
Method model can be obtained the recovery effects that mean square error is small and Y-PSNR is big by the algorithm model, complete quantum imaging.
The sparse imaging system of steady quantum provided by the invention and method have the following beneficial effects:
First, the present invention is provided with shaping optical path in quantum imaging optical path, can be filtered out not by high pass narrowband filter
The stray light needed improves imaging effect, and obtains stronger light beam using condenser lens to irradiate target, prevents from tangling light hair
It dissipates, number of photons information is only utilized in meeting calculating and does not utilize phase information, simplifies quantum imaging system；
Second, the gray scale picture loaded in traditional quantum imaging method in spatial light modulator is all by gaussian random
What matrix generated, it is unfavorable for storing, imaging all has uncertainty every time.Of the present invention is the random square of certainty
Battle array, it is only necessary to know that first element of matrix can construct matrix, reduce storage condition, and the feelings less in hits
The recovery image that effect is better than gaussian random matrix can be obtained under condition；
Third, the present invention perceive quantum imaging method compared to Ordinary Compression, have and eliminate systematic error, jamproof spy
Property, the imaging results obtained in practical situations are with more robustness.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of composition schematic diagram of the steady sparse imaging system of quantum provided in an embodiment of the present invention；
Fig. 2 is a kind of flow diagram of the steady sparse imaging method of quantum provided in an embodiment of the present invention；
Fig. 3 (a) is the schematic diagram of simulation objectives；
Fig. 3 (b) is the simulation result schematic diagram obtained when hits is 300 with GPSR algorithm；
Fig. 3 (c) is the simulation result schematic diagram obtained when hits is 300 with OMP algorithm；
Fig. 3 (d) is the simulation result schematic diagram obtained when hits is 300 with TLS algorithm；
Fig. 3 (e) is the simulation result schematic diagram obtained when hits is 300 with present invention method；
Fig. 4 (a) is the schematic diagram of target object to be restored；
The experimental result schematic diagram that Fig. 4 (b), which is hits, to be obtained with GPSR algorithm when being 1500；
The experimental result schematic diagram that Fig. 4 (c), which is hits, to be obtained with OMP algorithm when being 1500；
The experimental result schematic diagram that Fig. 4 (d), which is hits, to be obtained with present invention method when being 1500；
When Fig. 5 (a) is that hits changes, the least mean-square error of GPSR algorithm, OMP algorithm and present invention method
Situation of change comparison diagram；
When Fig. 5 (b) is that hits changes, the Y-PSNR of GPSR algorithm, OMP algorithm and present invention method becomes
Change situation comparison diagram.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Fig. 1 show a kind of composition schematic diagram of steady sparse imaging system of quantum provided in an embodiment of the present invention.
Referring to Fig. 1, imaging system provided in an embodiment of the present invention includes: laser 1, half-wave plate 2, bbo crystal 3, first
Condenser lens 4, beam splitter 5, the second condenser lens 7, spatial light modulator 8, the first single-photon detector 9, the second single-photon detecting
Survey device 10, Single Photon Counting card 11 and computer 12.
Wherein, laser 1, for emitting laser to half-wave plate 2；
Half-wave plate 2 for receiving the laser of the transmitting of laser 1, and generates polarised light, to 3 polarized light-emitting of bbo crystal；
Bbo crystal 3 be converted under Spontaneous Parametric to polarised light and be entangled for receiving the polarised light of the transmitting of half-wave plate 2
Light beam is twined, emits entangled light to the first condenser lens 4；
First condenser lens 4, for focusing the entangled light of the first condenser lens transmitting to enhance the light intensity of entangled light,
And then emit the entangled light by convergence to beam splitter；
Beam splitter 5 is divided into horizontal direction light to the entangled light by convergence for receiving through over-focusing entangled light
Beam and vertical direction light beam two-way light beam；Wherein, vertical direction light beam projects directive object 6 to be imaged after beam splitter, Vertical Square
Target beam is denoted as to light beam；Horizontal direction light beam projects directive spatial light modulator after beam splitter, and vertical direction light beam is denoted as
Reference beam；
First single-photon detector 9 for receiving through the target beam after object to be imaged, and detects wherein included
Photon, and then detection photon is sent to Single Photon Counting card；
Second condenser lens 7, for focusing reference beam, so that reference beam is radiated in spatial light modulator；
Spatial light modulator 8 carries out amplitude modulation to reference beam for loading gray scale picture, and using gray scale picture,
Modulation light beam is obtained, and emits modulation light beam to the second single-photon detector；Wherein, gray scale picture is according to pre-generated determination
Property random matrix is transformed；
Second single-photon detector 10 and detects photon wherein included for receiving modulation light beam, and then to time phase
It closes single photon counting card and sends detection photon；
Single Photon Counting card 11, the spy sent for the first single-photon detector and the second single-photon detector
Photon is surveyed, and coincidence counting is carried out to the two, obtains corresponding coincidence counting value, and send coincidence counting value to computer；
Computer 12, for receiving coincidence counting value, so that it is random according to coincidence counting value and pre-generated certainty
Matrix is treated imaging object and is imaged using quantum imaging model, obtains and shows imaging picture.
Wherein, it should be noted that the working principle of spatial light modulator specifically: spatial light modulator includes many only
Vertical unit, they are spatially arranged in one-dimensional or two-dimensional array, and each unit can independently received optics control signal
Or electrical control signals, and change the optical property of itself by this control signal, to be adjusted to the light wave irradiated on it
System.In the present embodiment, gray scale picture of the load in spatial light modulator is corresponding electrical control signals, the ash of load
It is different to spend picture, then the optical property of each separate unit namely corresponding difference, and then the light wave of irradiation on it is adjusted
The amplitude namely difference of system.
Based on above-mentioned imaging system, the embodiment of the invention also provides a kind of steady sparse imaging method of quantum, applications
It is that the embodiment of the invention also provides a kind of steady sparse imaging methods of quantum in such as above-mentioned imaging system, shown in Fig. 2
Flow diagram.
Referring to fig. 2, the sparse imaging method of steady quantum provided in an embodiment of the present invention the following steps are included:
Step 1, M certainty random matrix is generated, and converts corresponding M gray scale for M certainty random matrix
Picture.
Wherein, the dimension of each certainty random matrix is N × N-dimensional, and N × N indicates that preset imaging resolution, N are positive
Integer, N > 1.
In a kind of concrete implementation mode, step 1 specifically includes following sub-step:
Step 1.1, setting M different initial values, according to the corresponding N × N-dimensional certainty of each forming initial fields with
Machine matrix, to obtain M certainty random matrix.
Wherein, it according to the corresponding N × N-dimensional certainty random matrix of each forming initial fields, specifically includes:
Using initial value as the first element of certainty random matrix；For the N in addition to first element2- 1 element, root
Its value is determined according to the functional relation of itself and first element；
Wherein it is determined that first element and remaining N in property random matrix2The functional relation of -1 element can indicate are as follows: xn+1
=f (af-1(xn)), yn=f (bf-1(xn)), f (x) takes sin x, sin in formula2X, cos x, cos2Any function, a=p/q in x
> 2, b=qJ, a, b are relatively prime improper fraction, and b indicates control parameter.
Step 1.2, M certainty random matrix is normalized respectively, obtains corresponding M gray scale picture.
Step 2, M gray scale picture is successively loaded onto spatial light modulator, so that spatial light modulator utilizes M gray scale
Picture carries out amplitude modulation to reference beam, obtains M amplitude different modulating light beam, and then make Single Photon Counting card
Obtain M different coincidence counting values.
Step 3,1 × N is converted by each certainty random matrix2The row vector of dimension obtains M 1 × N2The row of dimension to
Amount, and using wherein each row vector as a line of matrix to get to a M × N2The matrix of dimension is denoted as calculation matrix A；By M
A different coincidence counting value is write as a column vector, is denoted as measured value C.
Step 4, according to calculation matrix A, measured value C, quantum imaging model: C=(A+ △ A) × T+ △ E is established.
Wherein, T indicates target column vector, the lattice point error and modulation error that Δ A representation space optical modulator occurs, △ E
Indicate interference and systematic error.
Above-mentioned quantum imaging model: C=(A+ △ A) × T+ △ E derivation process is given below:
Firstly, pair correlation function is described below:
Analyzing and associating imaging formula, ignores the frequency association of photon pair, and entangled photon pairs can be with following wave function come table
Show:
In formula,Indicate two-photon wave function,Indicate the lateral wave vector component of target beam,Indicate reference beam
Lateral wave vector component,Indicate the Fourier transformation of the generation operator of target beam,Indicate the generation of reference beam
The Fourier transformation of operator, δ () indicate impulse function, | > indicate state function.
Wherein:WithIt is respectively as follows:
In formula, xsIndicate the spatial position coordinate of the target beam of injection beam splitter, xiIndicate the reference light of injection beam splitter
The spatial position coordinate of beam, j indicate imaginary unit.
The photon that parametric down conversion generates is associated with tangling to having position association simultaneously.
The then modulation function of target optical path are as follows:
H (x, xs)=∫ d α h (α, xs) h (x, α)
In formula, x indicates that the spatial position coordinate of the first single-photon detector, α indicate the spatial position coordinate of target object,
h(x1, x2) representation space position coordinates x1To spatial position coordinate x2Optical path modulation function, x1And x2Two are indicated in optical path
Different spatial position coordinates.
The modulation function of reference path are as follows:
H (x, xi)=∫ d β d ρ h (β, xi) h (ρ, β) h (y, ρ) L (β),
In formula, β indicates the position coordinates of the second condenser lens, the spatial position coordinate of ρ representation space optical modulator, y table
Show the spatial position coordinate of the second single-photon detector.
The two-photon wave function that detector detects can indicate are as follows:
φ (x, y)=∫ dxsdxiH (x, xs) T (α) h (y, xi)(Ai(ρ)+ΔA)+ΔE
=∫ dxsdxiD α d β d ρ h (α, xs) T (α) h (x, α)
* h (y, ρ) (Ai(ρ)+Δ A) h (ρ, β) L (β) h (β, xi)ψ(xs, xi)+Δ E,
Wherein, free space transmission function is h (x, x ') ≈ exp (i π/(d1λ)(x′-x)2)；Optical lens transmission function
Are as follows: L (β)=exp (i π/(λ f) β2)；T (α) indicates object penetrating function；AiThe gray scale loaded on (ρ) representation space optical modulator
The corresponding matrix of picture；The lattice point error and modulation error that Δ A representation space optical modulator occurs；Δ E indicates interference and system
Error；By converted under Spontaneous Parametric generate tangle two-photon state and can be approximately: ψ (xs, xi)≈δ(xs-xi), while optical path
Meet imaging formula: (d1+d4)+1/d2=1/f, wherein d1For reference arm lens to beam splitter distance；d4For target to point
The distance of beam device；d2For reference arm lens to spatial light modulator distance；F is the focal length of lens.
By two-photon wave functions expansion are as follows:
Gauss integration can approximation be written as:
So two-photon wave function simplifies are as follows:
Meet function are as follows:
In formula, AmIndicate calculation matrix, T (αn) indicate target column vector.
Then, meet function to simplify are as follows:
C=(A+ △ A) × T+ △ E.
Step 5, building and solving optimization problem:Obtain mesh
The sparse transformation vector x of column vector T is marked, and according to transformation of coefficient vector x and sparse basis Ψ, obtains target column vector T=Ψ
x。
Wherein, Ψ indicates sparse basis,Indicate cost function, λ | | x | |1For regularization term, λ indicates regularization
Coefficient, | | | |FIndicate Frobenius norm, | | | |1Indicate L1 norm.
Specifically, alternating iteration descent method, which can be used, solves above-mentioned optimization problem.The basic think of of alternating iteration descent method
Want to fix a parameter between E and x, optimizing another parameter, continuous alternative optimization, until reaching stop condition.
Specifically, it is assumed that E (i) has been arrived in i-th optimization, then fixes E (i), solves the optimization problem about x (i):It, can be with as can be seen that this is a classical LASSO linear regression problem
Efficient Solution is carried out using convex optimization tool packet sedumi or cvx.
After having obtained the x (i) of i-th optimization, it would be desirable to estimate E (i+1), optimization problem is
For such quadratic function problem, minimum point is it
Stationary point solvesAcquire closed solutions E (i+1)=[y-Ax (i)] xH(xxH
+I)-1。
Step 6, target column vector T is reduced to N × N-dimensional matrix to get the image of object to be imaged is arrived.
So far, imaging method provided in an embodiment of the present invention terminates.
Above-mentioned imaging system and method based on the embodiment of the present invention, by the laser that issues laser through filtering
Play on bbo crystal generation after wave and polarization adjustment polarization direction is mutually perpendicular and tangle two-photon pair, then passes through beam splitter
Light beam is divided into two-way, light beam shines in target all the way, referred to as target beam；Another way light beam is adjusted by spatial light modulator
System, referred to as reference beam.By single-photon detector by two-way photon collection, be transferred in Single Photon Counting card into
Row match operation obtains multiple coincidence counting values by changing observing matrix of the load in spatial modulator；It considers further that and is
Error of uniting and interference, model imaging formula again, obtain a kind of sparse steady calculation suitable under actual conditions
Method model can be obtained the recovery effects that mean square error is small and Y-PSNR is big by the algorithm model, complete quantum imaging.
The sparse imaging system of steady quantum provided by the invention and method have the following beneficial effects:
First, the present invention is provided with shaping optical path in quantum imaging optical path, can be filtered out not by high pass narrowband filter
The stray light needed improves imaging effect, and obtains stronger light beam using condenser lens to irradiate target, prevents from tangling light hair
It dissipates, number of photons information is only utilized in meeting calculating and does not utilize phase information, simplifies quantum imaging system；
Second, the gray scale picture loaded in traditional quantum imaging method in spatial light modulator is all by gaussian random
What matrix generated, it is unfavorable for storing, imaging all has uncertainty every time.Of the present invention is the random square of certainty
Battle array, it is only necessary to know that first element of matrix can construct matrix, reduce storage condition, and the feelings less in hits
The recovery image that effect is better than gaussian random matrix can be obtained under condition；
Third, the present invention perceive quantum imaging method compared to Ordinary Compression, have and eliminate systematic error, jamproof spy
Property, the imaging results obtained in practical situations are with more robustness.
Imaging effect of the invention is illustrated below by emulation and its result:
Emulation experiment one:
1, parameter setting
For the image to be restored referring to Fig. 3 (a), which is 64 × 64, and the sparse transformation used is small echo change
It changes.In optimization problemThe maximum value of picture gray scale be 255, hits 300, with OMP algorithm,
GPSR algorithm, TLS algorithm and present invention method carry out image recovery to Fig. 3 (a).
2, experiment content
Image recovery effects are assessed using Y-PSNR, Y-PSNR is bigger, and recovery effects are better.Wherein, peak
It is worth signal-to-noise ratio is defined as:
In formula, y 'ijAnd yijIt is expressed as the pixel position of the image restored and original image.
To picture shown in Fig. 3 (a) using OMP algorithm, GPSR algorithm, TLS algorithm and present invention method into
Row simulation process, Fig. 3 (b) are the recovery image that GPSR algorithm obtains, and Y-PSNR 27.1223dB, Fig. 3 (c) are OMP calculation
The recovery image that method obtains, Y-PSNR 30.8589dB, Fig. 3 (d) are the recovery image that TLS algorithm obtains, peak value noise
Than being the recovery image that present invention method obtains, Y-PSNR 49.8627dB for 32.5639dB, Fig. 3 (e).It is right
Than can be seen that, present invention method adds interference and noise in the picture and hits can be compared under the same conditions
Ordinary Compression perception algorithm effect preferably restores image, can preferably inhibit interference and noise.
Emulation experiment two:
1, parameter setting
The power adjustment of coherent laser is 300mw, and the time of each coincidence counting accumulation is 15s.Observing matrix size
It is 64 × 64, the image recovered is also same size；M gray scale pictures, load are generated with certainty random matrix
In spatial light modulator, M is sampling number, takes M=1500 here；1 detection efficient of single-photon detector is 5.05 × 104Light
Subnumber/second, 2 detection efficient of single-photon detector are 5.10 × 104Number of photons/second.
2, experiment content
Target object shown in Fig. 4 (a) is restored using present invention method, and is missed using lowest mean square
Poor (MSE) and peak-peak signal-to-noise ratio (PSNR) measure image recovery effects, and MSE is smaller, PSNR is bigger, image recovery effects
Better.Wherein, MSE and PSNR formula is as follows:
Fig. 4 (a) is the schematic diagram of target object to be restored, and material object has the steel plate of double slit for one piece, will be impermeable on steel plate
Bright local gray value is taken as 0, and double slit position gray value is taken as 255.
When hits is 1500, image and Fig. 4 (c) that the GPSR algorithm of Fig. 4 (b) restores can be clearly seen that
The image that OMP algorithm restores is all very fuzzy, and there are a large amount of desultory points, and the present invention method of Fig. 4 (d) can obtain very
Good recovery imaging effect.Further, it is also possible to found out from Fig. 5 (a) with sampling transformation of variables, present invention method
MSE wants low more than traditional compressed sensing OMP, GPSR algorithm, with the increase of hits, the embodiment of the present invention in Fig. 5 (b)
PSNR ratio OMP, GPSR algorithm of method is much higher, can intuitively find out from the numerical value change of MSE and PSNR of the invention real
Applying a method can be good at restoring target object.
To sum up, above-mentioned emulation experiment through the embodiment of the present invention, demonstrate the method for the embodiment of the present invention correctness,
Validity and reliability.
Those of ordinary skill in the art will appreciate that: realize that all or part of the steps of above method embodiment can pass through
The relevant hardware of program instruction is completed, and program above-mentioned can be stored in a computer readable storage medium, the program
When being executed, step including the steps of the foregoing method embodiments is executed；And storage medium above-mentioned includes: ROM, RAM, magnetic disk or light
The various media that can store program code such as disk.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (4)
1. a kind of sparse imaging system of steady quantum characterized by comprising laser, half-wave plate, bbo crystal, first gather
Focus lens, beam splitter, the second condenser lens, spatial light modulator, the first single-photon detector, the second single-photon detector, when
Between correlated single photon numbered card and computer；
Wherein, the laser, for emitting laser to the half-wave plate；
The half-wave plate for receiving the laser of the laser transmitting, and generates polarised light, emits institute to the bbo crystal
State polarised light；
The bbo crystal carries out under Spontaneous Parametric the polarised light for receiving the polarised light of the half-wave plate transmitting
It is converted to entangled light, emits entangled light to first condenser lens；
First condenser lens, for focusing the entangled light of the first condenser lens transmitting to enhance the light of entangled light
By force, and then to the beam splitter emit the entangled light by convergence；
The beam splitter, it is described through over-focusing entangled light for receiving, water is divided into the entangled light by convergence
Square to light beam and vertical direction light beam two-way light beam；Wherein, directive is to be imaged after vertical direction light beam projects the beam splitter
Object, vertical direction light beam are denoted as target beam；Space light modulation described in directive after the horizontal direction light beam injection beam splitter
Device, vertical direction light beam are denoted as reference beam；
First single-photon detector for receiving through the target beam after object to be imaged, and detects wherein included
Photon, and then detection photon is sent to the Single Photon Counting card；
Second condenser lens, for focusing the reference beam, so that the reference beam is radiated at spatial light modulator
On；
The spatial light modulator carries out amplitude tune to the reference beam for loading gray scale picture, and using gray scale picture
System obtains modulation light beam, and emits the modulation light beam to second single-photon detector；Wherein, the gray scale picture root
It is transformed according to pre-generated certainty random matrix；
Described second single-photon detector for receiving the modulation light beam, and detects photon wherein included, and then to described
Single Photon Counting card sends detection photon；
The Single Photon Counting card is sent out for first single-photon detector and second single-photon detector
The detection photon sent, and coincidence counting is carried out to the two, corresponding coincidence counting value is obtained, and send the symbol to the computer
Total numerical value；
The computer, for receiving the coincidence counting value, and then according to the coincidence counting value and described pre-generated
Certainty random matrix is imaged the object to be imaged using quantum imaging model, obtains and shows imaging picture.
2. a kind of sparse imaging method of steady quantum is applied to imaging system as described in claim 1, which is characterized in that
It the described method comprises the following steps:
Step 1, M certainty random matrix is generated, and converts corresponding M gray scale for the M certainty random matrix
Picture；Wherein, the dimension of each certainty random matrix is N × N-dimensional, and N × N indicates preset imaging resolution, and N is positive whole
Number, N > 1；
Step 2, the M gray scale picture is successively loaded onto spatial light modulator, so that spatial light modulator utilizes the M
Gray scale picture carries out amplitude modulation to the reference beam, obtains M amplitude different modulating light beam, and then make time correlation monochromatic light
Sub-count card obtains M different coincidence counting values；
Step 3,1 × N is converted by each certainty random matrix2The row vector of dimension obtains M 1 × N2The row vector of dimension, and
Using wherein each row vector as a line of matrix to get to a M × N2The matrix of dimension is denoted as calculation matrix A；By the M
A different coincidence counting value is write as a column vector, is denoted as measured value C；
Step 4, according to the calculation matrix A, the measured value C, quantum imaging model: C=(A+ Δ A) × T+ Δ E is established；Its
In, T indicate target column vector, Δ A representation space optical modulator occur lattice point error and modulation error, Δ E indicate interference and
Systematic error；
Step 5, building and solving optimization problem:Obtain target column
The sparse transformation vector x of vector T；According to the transformation of coefficient vector x and sparse basis Ψ, target column vector T=Ψ x is obtained；
Wherein, Ψ indicates sparse basis,Indicate cost function, λ | | x | |1For regularization term, λ indicates regularization system
Number, | | | |FIndicate Frobenius norm, | | | |1Indicate L1 norm；
Step 6, the target column vector T is reduced to N × N-dimensional matrix to get the image of object to be imaged is arrived.
3. according to the method described in claim 2, it is characterized in that, step 1 specifically includes following sub-step:
Step 1.1, M different initial values of setting, according to the random square of the corresponding N × N-dimensional certainty of each forming initial fields
Battle array, to obtain M certainty random matrix；
Step 1.2, the M certainty random matrix is normalized respectively, obtains corresponding M gray scale picture.
4. described corresponding according to each forming initial fields according to the method described in claim 3, it is characterized in that, in step 1.1
One N × N-dimensional certainty random matrix, specifically includes:
Using the initial value as the first element of certainty random matrix；For the N in addition to the first element2- 1 element,
Its value is determined according to the functional relation of itself and first element；
Wherein it is determined that first element and remaining N in property random matrix2The functional relation of -1 element can indicate are as follows: xn+1=f
(af-1(xn)), yn=f (bf-1(xn)), f (x) takes sin x, sin in formula2X, cos x, cos2Any function in x, a=p/q >
2, b=qJ, a, b are relatively prime improper fraction, and b indicates control parameter.
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