CN109115681B - Stable quantum sparse imaging system and method - Google Patents
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Abstract
The invention belongs to the technical field of quantum imaging, and discloses a stable quantum sparse imaging system and a method, wherein the system comprises: the device comprises a laser, a half-wave plate, a BBO crystal, a first focusing lens, a beam splitter, a second focusing lens, a spatial light modulator, a first single-photon detector, a second single-photon detector, a time-dependent single-photon counting card and a computer. The invention can ensure the imaging robustness under the condition of interference and system error.
Description
Technical Field
The invention belongs to the technical field of quantum imaging, and relates to a stable quantum sparse imaging system and a stable quantum sparse imaging method, in particular to a quantum sparse imaging method and a quantum sparse imaging device which are based on entangled two photons and are stable to system errors and interference.
Background
Quantum imaging, as a novel imaging technique, utilizes quantum entanglement to enable mutually independent signal space and reference space to transmit object image information of one space, so quantum imaging is also called correlated imaging or ghost imaging.
In conventional imaging, there are mainly three defects: 1) the imaging resolution is limited by the rayleigh diffraction limit; 2) imaging requires receiving two-dimensional scan data of an image with an area detector; 3) interference and noise easily affect imaging, so that the resolution of an imaging result is low. The advent of quantum imaging technology has made up for these deficiencies, representing a great advantage: 1) the resolution of quantum imaging can break through the Rayleigh limit, thereby achieving the purpose of super resolution; 2) the quantum imaging can be completed only by two single-photon detectors without using a planar detector, so that the quantum imaging device is suitable for the condition that the planar detector with large volume cannot be used, and the cost is saved; 3) the target path and the reference path in the quantum imaging device are separated, so that the quantum imaging device has certain anti-interference capability, and the imaging by utilizing the correlation characteristic has the anti-interference advantage compared with the traditional optical imaging. Therefore, quantum imaging has wide application prospect in the fields of military remote sensing detection, medical imaging, voice transmission, wireless communication and the like. Meanwhile, quantum imaging also has defects, such as expensive equipment, long sampling coincidence time, large data processing capacity and the like.
The compressed sensing theory is a brand-new method for acquiring signals and images, which is proposed by D.Donoho, J.Romberg, E.Candes and the like, and the compressed sensing theory provides that when signals are processed, data can be transformed to a certain transform domain, the transform domain is sparse, data compression can be carried out, the limit of Nyquist sampling law is broken through, and then a compressed sensing iterative optimization reconstruction algorithm is utilized to reconstruct the signals of the sparse domain to obtain the required original signal imaging effect. The compressive sensing theory is applied to quantum imaging, so that a better imaging effect can be obtained under the condition of less sampling number, and the imaging time is effectively shortened.
In the current quantum imaging compressed sensing theory, entangled two photons generated by spontaneous parametric down-conversion are used as a Light source, a reference path Light source is modulated by a random pattern loaded by a Spatial Light Modulator (SLM), and then is subjected to coincidence counting with a Light source of a target path, and an original image is obtained by reconstruction. Generally, a random matrix is selected as an observation matrix, and because the random matrix has uncertainty and cannot be stored, the difference of the recovery effect of each imaging is large, and the recovery effect is not good under the condition of less sampling number. In addition, in the actual imaging process, system errors and interference are unavoidable, and both the system errors and the interference can cause deviation of coincidence counting of the existing method, so that the imaging effect is reduced.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a stable quantum sparse imaging system and method, which can ensure the stability of imaging under the condition of interference and system errors.
In order to achieve the purpose of the method, the invention adopts the following technical scheme to realize:
in a first aspect, a robust quantum sparse imaging system is provided, comprising: the device comprises a laser, a half-wave plate, a BBO crystal, a first focusing lens, a beam splitter, a second focusing lens, a spatial light modulator, a first single-photon detector, a second single-photon detector, a time-dependent single-photon counting card and a computer;
the laser is used for emitting laser to the half-wave plate;
the half-wave plate is used for receiving the laser emitted by the laser, generating polarized light and emitting the polarized light to the BBO crystal;
the BBO crystal is used for receiving the polarized light emitted by the half-wave plate, performing spontaneous parameter down-conversion on the polarized light to obtain an entangled light beam, and emitting the entangled light beam to the first focusing lens;
the first focusing lens is used for focusing the entangled light beam emitted by the first focusing lens so as to enhance the light intensity of the entangled light beam and further emit the converged entangled light beam to the beam splitter;
the beam splitter is used for receiving the focused entangled light beams and splitting the converged entangled light beams into two paths of light beams in a horizontal direction and a vertical direction; the light beam in the vertical direction is emitted out of the beam splitter and then emitted to an object to be imaged, and the light beam in the vertical direction is marked as a target light beam; the horizontal light beam is emitted out of the beam splitter and then emitted to the spatial light modulator, and the vertical light beam is marked as a reference light beam;
the first single-photon detector is used for receiving the target light beam which penetrates through the object to be imaged, detecting photons contained in the target light beam and further sending detected photons to the time-dependent single-photon counting card;
the second focusing lens is used for focusing the reference beam so as to enable the reference beam to be irradiated on the spatial light modulator;
the spatial light modulator is used for loading a gray picture, carrying out amplitude modulation on the reference light beam by using the gray picture to obtain a modulated light beam and transmitting the modulated light beam to the second single-photon detector; the gray level picture is converted according to a deterministic random matrix generated in advance;
the second single-photon detector is used for receiving the modulated light beam, detecting photons contained in the modulated light beam and further sending detected photons to the time-dependent single-photon counting card;
the time correlation single-photon counting card is used for detecting photons sent by the first single-photon detector and the second single-photon detector, performing coincidence counting on the photons to obtain corresponding coincidence counting values, and sending the coincidence counting values to the computer;
and the computer is used for receiving the coincidence counting value, and then imaging the object to be imaged by using a quantum imaging model according to the coincidence counting value and the pre-generated deterministic random matrix to obtain and display an imaging picture.
In a second aspect, a robust quantum sparse imaging method is provided, comprising the following steps:
step 1, generating M deterministic random matrices, and converting the M deterministic random matrices into corresponding M gray level pictures; the dimension of each deterministic random matrix is NxN, the NxN represents preset imaging resolution, N is a positive integer, and N is more than 1;
step 2, sequentially loading the M gray level pictures to a spatial light modulator so that the spatial light modulator performs amplitude modulation on the reference light beam by using the M gray level pictures to obtain M modulated light beams with different amplitudes, and further enabling a time-dependent single photon counting card to obtain M different coincidence count values;
step 3, converting each deterministic random matrix into 1 XN2Dimension of row vector to obtain M pieces of 1 XN2Dimension row vectors, and taking each row vector as a row of the matrix to obtain an M × N2A matrix of dimensions, denoted as measurement matrix a; writing the M different coincidence counting values into a column vector, and recording the column vector as a measured value C;
step 4, establishing a quantum imaging model according to the measurement matrix A and the measurement value C: c ═ a + Δ a) × T + Δ E; wherein, T represents a target column vector, Delta A represents a lattice point error and a modulation error of the spatial light modulator, and Delta E represents interference and a system error;
and 5, constructing and solving an optimization problem:
obtaining a sparse transformation vector x of the target column vector T; obtaining a target column vector T ═ Ψ x according to the coefficient transformation vector x and the sparse basis Ψ;
wherein Ψ represents a sparse group,
representing a cost function, lambda | x | non-woven phosphor1As a regularization term, λ represents a regularization coefficient, | | | | | luminanceFRepresents the Frobenius norm, | | | | | | luminance1Represents the norm L1
And 6, reducing the target column vector T into an NxN-dimensional matrix to obtain an image of the object to be imaged.
Based on the steady quantum sparse imaging system and the steady quantum sparse imaging method provided by the invention, laser emitted by a laser is filtered and subjected to polarization adjustment, and then the laser is irradiated on a BBO crystal to generate entangled two-photon pairs with mutually vertical polarization directions, and then the light beam is divided into two paths by a beam splitter, wherein one path of light beam irradiates a target and is called a target light beam; the other beam is modulated by a spatial light modulator, called the reference beam. Collecting two paths of photons through a single photon detector, transmitting the photons to a time-correlated single photon counting card for coincidence operation, and obtaining a plurality of coincidence counting values by changing an observation matrix loaded on a spatial modulator; and then, taking system errors and interference into consideration, modeling the imaging formula again to obtain a sparse and steady algorithm model suitable for practical conditions, and obtaining a recovery effect with small mean square error and large peak signal-to-noise ratio through the algorithm model to complete quantum imaging.
The robust quantum sparse imaging system and method provided by the invention have the following beneficial effects:
firstly, the shaping optical path is arranged in the quantum imaging optical path, the high-pass narrow-band filter can filter out the unnecessary stray light to improve the imaging effect, the focusing lens is used for obtaining stronger light beams to irradiate a target, the entanglement light divergence is prevented, only photon number information and phase information are utilized in coincidence calculation, and a quantum imaging system is simplified;
secondly, in the conventional quantum imaging method, the gray-scale pictures loaded on the spatial light modulator are generated by a gaussian random matrix, which is not favorable for storage, and each imaging has uncertainty. The method adopts the deterministic random matrix, can construct the matrix only by knowing the first element of the matrix, reduces the storage condition, and can obtain the recovery image with the effect superior to that of the Gaussian random matrix under the condition of less sampling number;
thirdly, compared with the common compressed sensing quantum imaging method, the method has the characteristics of eliminating system errors and resisting interference, and the obtained imaging result is more stable under the actual condition.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram illustrating a robust quantum sparse imaging system according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of a robust quantum sparse imaging method according to an embodiment of the present invention;
FIG. 3(a) is a schematic diagram of a simulation target;
FIG. 3(b) is a diagram illustrating simulation results obtained by the GPSR algorithm when the number of samples is 300;
FIG. 3(c) is a diagram illustrating simulation results obtained by the OMP algorithm with a sampling number of 300;
FIG. 3(d) is a schematic diagram of the simulation results obtained with the TLS algorithm at a sample number of 300;
FIG. 3(e) is a diagram illustrating simulation results obtained by the method of the embodiment of the present invention when the sampling number is 300;
FIG. 4(a) is a schematic view of a target object to be recovered;
FIG. 4(b) is a diagram illustrating experimental results obtained by the GPSR algorithm when the number of samples is 1500;
FIG. 4(c) is a schematic diagram of experimental results obtained with the OMP algorithm for a sample number of 1500;
FIG. 4(d) is a schematic diagram showing experimental results obtained by the method of the embodiment of the present invention when the number of samples is 1500;
FIG. 5(a) is a comparison graph of minimum mean square error variation of the GPSR algorithm, the OMP algorithm and the method of the embodiment of the present invention when the sampling number varies;
fig. 5(b) is a comparison graph of the peak snr change of the GPSR algorithm, the OMP algorithm, and the method according to the embodiment of the present invention when the sampling number changes.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic composition diagram of a robust quantum sparse imaging system according to an embodiment of the present invention.
Referring to fig. 1, an imaging system provided by an embodiment of the present invention includes: the device comprises a laser 1, a half-wave plate 2, a BBO crystal 3, a first focusing lens 4, a beam splitter 5, a second focusing lens 7, a spatial light modulator 8, a first single-photon detector 9, a second single-photon detector 10, a time-dependent single-photon counting card 11 and a computer 12.
The laser 1 is used for emitting laser to the half-wave plate 2;
the half-wave plate 2 is used for receiving the laser emitted by the laser 1, generating polarized light and emitting the polarized light to the BBO crystal 3;
the BBO crystal 3 is used for receiving the polarized light emitted by the half-wave plate 2, performing spontaneous parameter down-conversion on the polarized light to obtain an entangled light beam, and emitting the entangled light beam to the first focusing lens 4;
the first focusing lens 4 is used for focusing the entangled light beams emitted by the first focusing lens so as to enhance the light intensity of the entangled light beams and further emit the converged entangled light beams to the beam splitter;
the beam splitter 5 is used for receiving the focused entangled light beams and splitting the converged entangled light beams into two paths of light beams, namely horizontal light beams and vertical light beams; wherein, the light beam in the vertical direction is emitted out of the beam splitter and then emitted to the object 6 to be imaged, and the light beam in the vertical direction is recorded as a target light beam; the horizontal light beam is emitted out of the beam splitter and then emitted to the spatial light modulator, and the vertical light beam is marked as a reference light beam;
the first single-photon detector 9 is used for receiving the target light beam which penetrates through the object to be imaged, detecting photons contained in the target light beam and further sending detected photons to the time-dependent single-photon counting card;
a second focusing lens 7 for focusing the reference beam so that the reference beam is irradiated on the spatial light modulator;
the spatial light modulator 8 is used for loading a gray level picture, carrying out amplitude modulation on the reference light beam by using the gray level picture to obtain a modulated light beam and transmitting the modulated light beam to the second single-photon detector; the gray level picture is converted according to a pre-generated deterministic random matrix;
the second single-photon detector 10 is used for receiving the modulated light beam, detecting photons contained in the modulated light beam and further sending detected photons to the time-dependent single-photon counting card;
the time correlation single-photon counting card 11 is used for detecting photons sent by the first single-photon detector and the second single-photon detector, performing coincidence counting on the photons to obtain corresponding coincidence counting values, and sending the coincidence counting values to a computer;
and the computer 12 is used for receiving the coincidence count value, and then imaging the object to be imaged by using the quantum imaging model according to the coincidence count value and the pre-generated deterministic random matrix to obtain and display an imaging picture.
It should be noted that the working principle of the spatial light modulator specifically includes: the spatial light modulator comprises a plurality of individual cells spatially arranged in a one-or two-dimensional array, each cell being capable of independently receiving an optical or electrical control signal and changing its optical properties in response to the control signal, thereby modulating the light waves impinging thereon. In this embodiment, the grayscale images loaded on the spatial light modulator are the corresponding electrical control signals, and if the loaded grayscale images are different, the optical properties of the individual units are correspondingly different, so that the amplitude of modulating the light waves irradiated thereon is different.
Based on the imaging system, the embodiment of the invention further provides a robust quantum sparse imaging method, which is applied to the imaging system, and fig. 2 is a schematic flow diagram of the robust quantum sparse imaging method provided by the embodiment of the invention.
Referring to fig. 2, the robust quantum sparse imaging method provided by the embodiment of the present invention includes the following steps:
step 1, generating M deterministic random matrices, and converting the M deterministic random matrices into corresponding M gray level pictures.
Wherein the dimension of each deterministic random matrix is NXN, NXN represents the preset imaging resolution, N is a positive integer, and N is more than 1.
In a specific implementation manner, step 1 specifically includes the following sub-steps:
step 1.1, setting M different initial values, and generating a corresponding NxN-dimensional deterministic random matrix according to each initial value, thereby obtaining M deterministic random matrices.
Generating a corresponding N × N deterministic random matrix according to each initial value, specifically including:
taking the initial value as the first element of the deterministic random matrix; for N other than the first element2-1 element, the value of which is determined according to its functional relationship with the first element;
wherein the first element and the rest N in the deterministic random matrix21 element ofThe functional relationship may be expressed as: x is the number ofn+1＝f(af-1(xn))，yn＝f(bf-1(xn) In the formula, f (x) is sin x, sin2x，cos x，cos2x, a ═ p/q > 2, b ═ qJA and b are relatively prime false scores, and b represents a control parameter.
And step 1.2, respectively carrying out normalization processing on the M deterministic random matrixes to obtain corresponding M gray level pictures.
And 2, sequentially loading the M gray level pictures to the spatial light modulator so that the spatial light modulator performs amplitude modulation on the reference light beam by using the M gray level pictures to obtain M modulated light beams with different amplitudes, and further enabling the time-dependent single photon counting card to obtain M different coincidence count values.
Step 3, converting each deterministic random matrix into 1 XN2Dimension of row vector to obtain M pieces of 1 XN2Dimension row vectors, and taking each row vector as a row of the matrix to obtain an M × N2A matrix of dimensions, denoted as measurement matrix a; the M different coincidence count values are written as a column vector, denoted as measurement C.
Step 4, establishing a quantum imaging model according to the measurement matrix A and the measurement value C: c ═ a + Δ a) × T + Δ E.
Where T denotes a target column vector, Δ a denotes a lattice error and a modulation error occurring in the spatial light modulator, and Δ E denotes interference and a system error.
The quantum imaging model described above is given below: derivation of (a + Δ a) × T + Δ E:
first, the correlation function is described as follows:
analyzing the correlation imaging formula, ignoring the frequency correlation of photon pairs, the entangled photon pairs can be represented by the following wave function:
in the formula (I), the compound is shown in the specification,
the two-photon wavelet function is represented,
representing the transverse wave-vector component of the target beam,
representing the transverse wave-vector component of the reference beam,
a fourier transform of a generator representing the object beam,
represents the Fourier transform of the operator generating the reference beam, δ () represents the impulse function, | ·>Representing a state function.
Wherein:
and
respectively as follows:
in the formula, xsRepresenting the spatial position coordinate, x, of the target beam exiting the beam splitteriRepresenting the spatial location coordinates of the reference beam exiting the beam splitter and j represents the imaginary unit.
The photon pairs generated by parametric down-conversion have both position and entanglement associations.
The modulation function of the target optical path is then:
h(x，xs)＝∫dαh(α，xs)h(x，α)
wherein x represents the spatial position coordinates of the first single-photon detector, α represents the spatial position coordinates of the target object, and h (x)1，x2) Representing spatial position coordinates x1To spatial position coordinate x2Of the optical path of (1), x1And x2Representing two different spatial location coordinates in the optical path.
The modulation function of the reference optical path is:
h(x，xi)＝∫dβdρh(β，xi)h(ρ，β)h(y，ρ)L(β)，
where β denotes the position coordinate of the second focusing lens, ρ denotes the spatial position coordinate of the spatial light modulator, and y denotes the spatial position coordinate of the second single-photon detector.
The bifocal wavelet function detected by the detector can be expressed as:
φ(x，y)＝∫dxsdxih(x，xs)T(α)h(y，xi)(Ai(ρ)+ΔA)+ΔE
＝∫dxsdxidαdβdρh(α，xs)T(α)h(x，α)*h(y，ρ)(Ai(ρ)+ΔA)h(ρ，β)L(β)h(β，xi)ψ(xs，xi)+ΔE，
wherein the free space transfer function is h (x, x') ≈ exp (i pi/(d)1λ)(x′-x)2) (ii) a The optical lens transfer function is: l (β) ═ exp (i pi/(λ f) β2) (ii) a T (α) represents a target transmission function; a. thei(ρ) represents a matrix corresponding to the grayscale picture loaded on the spatial light modulator; Δ a represents a lattice error and a modulation error occurring in the spatial light modulator; Δ E represents interference and system error; the entangled two-photon states generated by spontaneous parametric down-conversion can be approximated as: psi (x)s，xi)≈δ(xs-xi) Meanwhile, the optical path satisfies the imaging formula: (d)1+d4)+1/d21/f, wherein d1The distance from the lens to the beam splitter for the reference path; d4Is the distance of the target to the beam splitter; d2The distance from the lens of the reference path to the spatial light modulator; f is the focal length of the lens.
The bifocal wavelet function is expanded as:
the gaussian integral can be approximately written as:
the bifocal wavelet function is reduced to:
the fitting function is:
in the formula, AmDenotes a measurement matrix, T (α)n) Representing the target column vector.
Then, the fitting function is simplified as:
C＝(A+ΔA)×T+ΔE。
and 5, constructing and solving an optimization problem:
and obtaining a sparse transformation vector x of the target column vector T, and obtaining the target column vector T as psi x according to the coefficient transformation vector x and the sparse basis psi.
Wherein Ψ represents a sparse group,
representing a cost function, lambda | x | non-woven phosphor1As a regularization term, λ represents a regularization coefficient, | | | | | luminanceFRepresents the Frobenius norm, | | | | | | luminance1Representing the L1 norm.
Specifically, the optimization problem can be solved by using an alternating iterative descent method. The basic idea of the alternative iterative descent method is to fix one parameter between E and x, optimize the other parameter, and continuously alternate the optimization until a stop condition is reached.
Specifically, assuming that the i is suboptimal to e (i), e (i) is fixed, and the optimization problem with respect to x (i) is solved:
it can be seen that this is a classical LASSO linear regression problem that can be solved efficiently using the convex optimization toolkit sedumi or cvx.
When the ith sub-optimal x (i) is obtained, we need to estimate E (i +1), and the optimization problem is
For such quadratic function problems, the minimum point is its stagnation point, i.e. the solution is made
Solving for the closed solution E (i +1) ═ y-ax (i)]xH(xxH+I)-1。
And 6, reducing the target column vector T into an NxN-dimensional matrix to obtain an image of the object to be imaged.
The imaging method provided by the embodiment of the invention is finished.
Based on the imaging system and method provided by the embodiment of the invention, laser emitted by a laser is filtered and polarization-adjusted and then is irradiated on a BBO crystal to generate entangled two-photon pairs with mutually vertical polarization directions, and then the light beam is divided into two paths by a beam splitter, wherein one path of light beam irradiates a target and is called a target light beam; the other beam is modulated by a spatial light modulator, called the reference beam. Collecting two paths of photons through a single photon detector, transmitting the photons to a time-correlated single photon counting card for coincidence operation, and obtaining a plurality of coincidence counting values by changing an observation matrix loaded on a spatial modulator; and then, taking system errors and interference into consideration, modeling the imaging formula again to obtain a sparse and steady algorithm model suitable for practical conditions, and obtaining a recovery effect with small mean square error and large peak signal-to-noise ratio through the algorithm model to complete quantum imaging.
The robust quantum sparse imaging system and method provided by the invention have the following beneficial effects:
firstly, the shaping optical path is arranged in the quantum imaging optical path, the high-pass narrow-band filter can filter out the unnecessary stray light to improve the imaging effect, the focusing lens is used for obtaining stronger light beams to irradiate a target, the entanglement light divergence is prevented, only photon number information and phase information are utilized in coincidence calculation, and a quantum imaging system is simplified;
secondly, in the conventional quantum imaging method, the gray-scale pictures loaded on the spatial light modulator are generated by a gaussian random matrix, which is not favorable for storage, and each imaging has uncertainty. The method adopts the deterministic random matrix, can construct the matrix only by knowing the first element of the matrix, reduces the storage condition, and can obtain the recovery image with the effect superior to that of the Gaussian random matrix under the condition of less sampling number;
thirdly, compared with the common compressed sensing quantum imaging method, the method has the characteristics of eliminating system errors and resisting interference, and the obtained imaging result is more stable under the actual condition.
The imaging effect of the present invention is explained by the simulation and the result thereof as follows:
simulation experiment I:
1. parameter setting
The image to be restored is shown in fig. 3(a), and the pixel size of the image is 64 × 64, and the sparse transform is adopted for wavelet transform. The maximum value of the picture gray scale in the optimization problem is 255, the sampling number is 300, and the image recovery is performed on the image in the step (a) in the invention by using an OMP algorithm, a GPSR algorithm, a TLS algorithm and a method in an embodiment of the invention.
2. Content of the experiment
And evaluating the image recovery effect by adopting the peak signal-to-noise ratio, wherein the larger the peak signal-to-noise ratio is, the better the recovery effect is. Wherein the peak signal-to-noise ratio is defined as:
y 'of formula (II)'ijAnd yijRespectively, as the pixel locations of the restored image and the original image.
The picture shown in fig. 3(a) is subjected to simulation processing by using an OMP algorithm, a GPSR algorithm, a TLS algorithm and the method of the embodiment of the present invention, fig. 3(b) is a restored image obtained by the GPSR algorithm, the peak signal-to-noise ratio is 27.1223dB, fig. 3(c) is a restored image obtained by the OMP algorithm, the peak signal-to-noise ratio is 30.8589dB, fig. 3(d) is a restored image obtained by the TLS algorithm, the peak signal-to-noise ratio is 32.5639dB, fig. 3(e) is a restored image obtained by the method of the embodiment of the present invention, and the peak signal-to-noise ratio is 49.8627 dB. Compared with the prior art, the method can obtain the recovered image with better effect than the common compressed sensing algorithm under the conditions of adding interference and noise in the image and the same sampling number, and can better inhibit the interference and the noise.
And (2) simulation experiment II:
1. parameter setting
The power of the coherent laser was adjusted to 300mw and the time for each coincidence count accumulation was 15 s. The observation matrix size is 64 multiplied by 64, and the recovered image has the same size; generating M gray-scale pictures by using a deterministic random matrix, loading the M gray-scale pictures on a spatial light modulator, wherein M is sampling times, and is 1500; the detection efficiency of the single photon detector 1 is 5.05 multiplied by 104Photon number/second, single photon detector 2 detection efficiency of 5.10 multiplied by 104Number of photons/second.
2. Content of the experiment
The method of the embodiment of the invention is adopted to recover the target object shown in fig. 4(a), and the minimum Mean Square Error (MSE) and the maximum peak signal-to-noise ratio (PSNR) are adopted to measure the image recovery effect, wherein the smaller the MSE and the larger the PSNR, the better the image recovery effect. Wherein, MSE and PSNR formulas are as follows:
fig. 4(a) is a schematic diagram of a target object to be restored, the object is a steel plate with double slits, the gray value of an opaque part on the steel plate is taken as 0, and the gray value of the position of the double slits is taken as 255.
When the sampling number is 1500, it can be clearly seen that the image restored by the GPSR algorithm of fig. 4(b) and the image restored by the OMP algorithm of fig. 4(c) are blurred, and a large number of stray points exist, and the method of the embodiment of the present invention of fig. 4(d) can obtain a good restored imaging effect. In addition, it can be seen from fig. 5(a) that along with the transformation of the sampling number, the MSE of the method according to the embodiment of the present invention is much lower than that of the conventional compressive sensing OMP and GPSR algorithms, and along with the increase of the sampling number in fig. 5(b), the PSNR of the method according to the embodiment of the present invention is much higher than that of the OMP and GPSR algorithms, and it can be intuitively seen from the numerical changes of the MSE and the PSNR that the method according to the embodiment of the present invention can well recover the target object.
In summary, the above simulation experiments in the embodiments of the present invention verify the correctness, validity and reliability of the method in the embodiments of the present invention.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (3)
1. A robust quantum sparse imaging method is applied to a robust quantum sparse imaging system, and the imaging system comprises: the device comprises a laser, a half-wave plate, a BBO crystal, a first focusing lens, a beam splitter, a second focusing lens, a spatial light modulator, a first single-photon detector, a second single-photon detector, a time-dependent single-photon counting card and a computer;
the laser is used for emitting laser to the half-wave plate;
the half-wave plate is used for receiving the laser emitted by the laser, generating polarized light and emitting the polarized light to the BBO crystal;
the BBO crystal is used for receiving the polarized light emitted by the half-wave plate, performing spontaneous parameter down-conversion on the polarized light to obtain an entangled light beam, and emitting the entangled light beam to the first focusing lens;
the first focusing lens is used for focusing the entangled light beams emitted by the BBO crystal so as to enhance the light intensity of the entangled light beams and further emit the converged entangled light beams to the beam splitter;
the beam splitter is used for receiving the focused entangled light beams and splitting the converged entangled light beams into two paths of light beams in a horizontal direction and a vertical direction; the light beam in the vertical direction is emitted out of the beam splitter and then emitted to an object to be imaged, and the light beam in the vertical direction is marked as a target light beam; the horizontal light beam is emitted out of the beam splitter and then emitted to the spatial light modulator, and the vertical light beam is marked as a reference light beam;
the first single-photon detector is used for receiving the target light beam which penetrates through the object to be imaged, detecting photons contained in the target light beam and further sending detected photons to the time-dependent single-photon counting card;
the second focusing lens is used for focusing the reference beam so as to enable the reference beam to be irradiated on the spatial light modulator;
the spatial light modulator is used for loading a gray picture, carrying out amplitude modulation on the reference light beam by using the gray picture to obtain a modulated light beam and transmitting the modulated light beam to the second single-photon detector; the gray level picture is converted according to a deterministic random matrix generated in advance;
the second single-photon detector is used for receiving the modulated light beam, detecting photons contained in the modulated light beam and further sending detected photons to the time-dependent single-photon counting card;
the time correlation single-photon counting card is used for detecting photons sent by the first single-photon detector and the second single-photon detector, performing coincidence counting on the photons to obtain corresponding coincidence counting values, and sending the coincidence counting values to the computer;
the computer is used for receiving the coincidence counting value, and then imaging the object to be imaged by utilizing a quantum imaging model according to the coincidence counting value and the pre-generated deterministic random matrix to obtain and display an imaging picture;
the method comprises the following steps:
step 1, generating M deterministic random matrices, and converting the M deterministic random matrices into corresponding M gray level pictures; the dimension of each deterministic random matrix is NxN, the NxN represents preset imaging resolution, N is a positive integer, and N is more than 1;
step 2, sequentially loading the M gray level pictures to a spatial light modulator so that the spatial light modulator performs amplitude modulation on the reference light beam by using the M gray level pictures to obtain M modulated light beams with different amplitudes, and further enabling a time-dependent single photon counting card to obtain M different coincidence count values;
step 3, converting each deterministic random matrix into 1 XN2Dimension of row vector to obtain M pieces of 1 XN2Dimension row vectors, and taking each row vector as a row of the matrix to obtain an M × N2A matrix of dimensions, denoted as measurement matrix a; writing the M different coincidence counting values into a column vector, and recording the column vector as a measured value C;
step 4, establishing a quantum imaging model according to the measurement matrix A and the measurement value C: c ═ a + Δ a) × T + Δ E; wherein, T represents a target column vector, Delta A represents a lattice point error and a modulation error of the spatial light modulator, and Delta E represents interference and a system error;
and 5, constructing and solving an optimization problem:
obtaining a sparse transformation vector x of the target column vector T; obtaining a target column vector T ═ Ψ x according to the sparse transformation vector x and the sparse basis Ψ;
wherein Ψ represents a sparse group,
representing a cost function, lambda | x | non-woven phosphor1As a regularization term, λ represents a regularization coefficient, | | | | | luminanceFRepresents the Frobenius norm, | | | | | | luminance1Represents the L1 norm;
and 6, reducing the target column vector T into an NxN-dimensional matrix to obtain an image of the object to be imaged.
2. The method according to claim 1, characterized in that step 1 comprises in particular the following sub-steps:
step 1.1, setting M different initial values, and generating a corresponding NxN-dimensional deterministic random matrix according to each initial value so as to obtain M deterministic random matrices;
and 1.2, respectively carrying out normalization processing on the M deterministic random matrixes to obtain corresponding M gray level pictures.
3. The method according to claim 2, wherein in step 1.1, the generating a corresponding N × N deterministic random matrix according to each initial value specifically includes:
taking the initial value as a first element of a deterministic random matrix; for N other than the first element2-1 element, the value of which is determined according to its functional relationship with the first element;
wherein the first element and the rest N in the deterministic random matrix21 element ofThe functional relationship is expressed as: x is the number ofn+1＝f(af-1(xn))，yn＝f(bf-1(xn) In the formula, f (x) is sinx, sin2x，cosx，cos2x, a ═ p/q > 2, b ═ qJA and b are relatively prime false scores, b represents a control parameter, and p, q, and J are constants respectively.
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