A Photon Counting Simulation Method for Three-Dimensional Single-Pixel Imaging

Abstract

The present invention discloses a photon counting simulation method for three-dimensional single-pixel imaging, comprising the following steps: using a specified coding pattern diagram, respectively completing corresponding simulation calculations in a simulation environment. From the photon perspective, with photons as the basic simulation unit, three-dimensional single-pixel imaging photon counting simulation is carried out based on the Monte Carlo principle, wherein a simulation module is established to realize the photon state values in each stage of the simulated three-dimensional single-pixel imaging. It solves the problem that when single-pixel imaging is applied to three-dimensional objects, extra data components caused by the three-dimensional topography are introduced into the measurement data of the photodetector, and it is difficult to complete the simulation calculation of such problems in the single-pixel imaging simulation algorithm at the pixel level.

Description

Technical Field

[0001] The present invention relates to the field of imaging technology, and specifically, to a photon counting simulation method for three-dimensional single-pixel imaging. Background Art

[0002] Nowadays, with the booming development of information technology, imaging technology, as an important way to obtain visual information, has been widely used. As one of the imaging technologies, single-pixel imaging (SPI) has attracted the attention of many domestic and foreign research scholars due to its obvious advantages. For the current SPI technology, remarkable research progress has been made in fields such as compressive imaging, anti-scattering degradation imaging in the atmospheric environment, and imaging for moving targets.

[0003] It is worth noting that in the research papers published so far, most of the imaging objects in the desktop optical platform experiments by scholars are flat sheet targets, so as to simulate the situation when the SPI optical system is working. However, in the actual scenario, the imaging objects we face are often three-dimensional objects with three-dimensional topographies, rather than ideal planar objects, and it is necessary to extend the SPI technology to the 3D imaging field to improve its practical generalization.

[0004] Currently, there is an algorithm technology called the photon statistical model based on Poisson distribution. Its technology lies in using the means of photon simulation counting to simulate the photon detection problem of single-photon detectors. Although the existing technologies are all based on photon simulation, these technologies are not applicable to three-dimensional single-pixel imaging. Because the focus of the above-mentioned technologies is on whether photons are received by the detector, which belongs to the "binary existence problem", rather than the "counting problem". Summary of the Invention

[0005] Aiming at the defects in the prior art, the purpose of the present invention is to solve the problem of three-dimensional single-pixel imaging based on photon simulation.

[0006] To solve the above problems, the present invention provides a photon counting simulation method for three-dimensional single-pixel imaging, including the following steps:

[0007] Adopt a specified coding pattern diagram and complete the corresponding simulation calculations in a simulation environment respectively:

[0008] From the photon perspective, taking photons as the basic simulation unit, perform photon counting simulation for three-dimensional single-pixel imaging based on the Monte Carlo principle, and establish a simulation module to realize the photon states in each stage of simulated three-dimensional single-pixel imaging.

[0009] Further, the inputs of the simulation module are: imaging environment definition and target object definition, where the imaging environment definition includes imaging distance, projection angle, instrument three-dimensional coordinates, noise parameters, attenuation coefficient of the propagation medium, coding pattern diagram; the target object definition includes the surface reflectivity of the target object and 3D topography parameters.

[0010] Further, the output of the simulation module is the sequence value of the optoelectronic signal of the single-pixel detector.

[0011] Further, the algorithm of the simulation module includes the following steps:

[0012] S1: Input loading and parameter initialization settings;

[0013] S2: Traverse each frame of the coding pattern diagram.

[0014] Among them, step S2 includes the following steps:

[0015] S2-1: Photon excitation and coding pattern diagram loading: Generate a photon group whose quantity follows a Poisson distribution;

[0016] S2-2: Spatial light modulator encodes the photon distribution: Determine whether the photons are successfully reflected through the micromirror array;

[0017] S2-3: Photon flight calculation: Calculate the landing position of the surviving photons on the target object surface through an iterative algorithm;

[0018] S2-4: Photon counting: Calculate whether the photons are received according to the reflectivity at the landing point and the detector receiving position.

[0019] Further, in step S2-3, the photon flight calculation includes the following steps:

[0020] S2-3-1: When the photons pass through the projection lens, use the corresponding lens PSF function to simulate their propagation trajectory;

[0021] S2-3-2: In the photon propagation medium, assume that its one-way transmittance coefficient for photons is σ, representing that the probability of photons successfully passing through the propagation medium is σ, and endow the photon with three-dimensional coordinate attribute parameters (x i , y i , z i ) during the entire propagation process. According to the three-dimensional coordinates (x i0 , y i0 , z i0 ) and flight direction vector (t x , t y , t z ) of the photons when they exit at the projection end, and then use the iterative algorithm to calculate its flight landing point (x i-end , yi-end , z i-end ).

[0022] Furthermore, the iterative algorithm is the Newton iterative algorithm.

[0023] Furthermore, the surface reflection coefficient at the flight landing point defined on the surface of the target is R(x i-end , y i-end , z i-end ),

[0024] where R = r a + k s r s + k d r d · cosθ

[0025] where r a is the environmental error term, k s r s is the diffuse reflection term, k d r d is the specular reflection term, θ is the angle between the outgoing direction and the normal, and x_i_end, y_i_end, z_i_end represent the landing point coordinates.

[0026] Furthermore, this technology can also be combined with deep learning to improve the accuracy of 3D imaging.

[0027] Furthermore, the present invention also proposes a photon counting simulation device for three-dimensional single-pixel imaging, on which a computer program is stored, and when the computer program is executed by a processor, it can implement the three-dimensional single-pixel imaging photon counting simulation method described in the present invention.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The present invention provides a research means using computer photon simulation. In some cases where imaging is difficult to achieve, computer simulation is used to provide sufficiently accurate data support. Since the Monte Carlo simulation method is adopted for three-dimensional single-pixel imaging, through data simulation and experimental analysis, it is proved that the correlation coefficients between the simulated simulation numerical results and the real sampling signals of the algorithm proposed in the present invention are greater than 0.85 when facing planar targets and three-dimensional targets, that is, the two are highly correlated, which proves the feasibility of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1a is a schematic diagram of the physical system of Monte Carlo simulation;

[0031] Figure 1b is a schematic diagram of the process of Monte Carlo simulation;

[0032] Figure 2 It is the probability distribution diagram of the number of photons excited in the embodiment of the present invention following the Poisson distribution;

[0033] Figure 3 It is the numerical comparison diagram of the simulated signal and the real signal in the embodiment of the present invention;

[0034] Figure 4 It is the schematic diagram of the principle of the reflection coefficient of the target surface in the embodiment of the present invention;

[0035] Figure 5 It is the schematic diagram of the imaging system device of SPI in the embodiment of the present invention;

[0036] Figure 6 It is the schematic diagram of the Newton iteration algorithm in the embodiment of the present invention;

[0037] Figure 7 It is the schematic diagram of the pseudo - code of the simulation module in the embodiment of the present invention;

[0038] Among them, 1. The average number N = 4000, 2. The average number N = 8000, 3. The average number N = 12000, 4. The real sampling signal: planar target, 5. The real sampling signal: three - dimensional target, 6. The simulation signal: planar target, 7. The simulation signal: three - dimensional target, 8. Target, 9. Lens, 10. Plane mirror, 11. Laser, 12. Coding mode, 13. Spatial light modulator, 14. Single - pixel detector, 15. Lens. Specific Embodiment

[0039] The following makes a detailed description of the embodiments of the present invention. It should be emphasized that the following description is merely exemplary and not intended to limit the scope of the present invention and its applications.

[0040] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0041] The embodiments of the present invention are based on the following principles:

[0042] We have noticed that whether it is the Shape from Shading (SFS) method, the three-dimensional reconstruction method based on Photometric Stereo (PS), or the recovery method based on Phase Measurement Profilometry (PMP), the key parameter they focus on is the error variable brought by the three-dimensional topography to the fluctuation signal of the light intensity sequence detected by a single-pixel detector. This is because when the target object is a three-dimensional solid object, the trajectory of photons during the imaging process will change complexly due to the uneven surface information of the target object. From the perspective of signals, it is to introduce a component of the light intensity fluctuation signal determined by the target surface topography into the fluctuation signal of the light intensity sequence detected by the back-end device. From the microscopic perspective of photons, it is specifically manifested as follows: The photon group excited by the laser and the spatial light modulator passes through the projection lens and the scattering medium of the imaging environment, reaches the surface of the target object and is reflected, and finally the surviving photons are received by the single-pixel detector.

[0043] In the embodiments of the present invention, from the perspective of photons, a three-dimensional single-pixel imaging photon counting simulation method based on the Monte Carlo principle with photons as the basic simulation unit is proposed. This method explains the influence of the target three-dimensional topography on photon counting and performs quantitative representation of the optoelectronic signal value.

[0044] The innovation point of the embodiments of the present invention lies in designing an embedded algorithm for 3D-SPI. In the defined environment, as long as the coding mode is input, the digital result of the optoelectronic signal detection of the specified three-dimensional target object in the simulation environment can be obtained, providing an important technical means for the research of 3D-SPI. By introducing an accurate photon reflection model, this embodiment is applicable to three-dimensional single-pixel imaging and provides an important research means for the application of single-pixel imaging technology in the three-dimensional field.

[0045] 1.1 Photon simulation and simulation method based on the Monte Carlo principle

[0046] Monte Carlo simulation is a computer simulation method supported by the law of large numbers in probability statistics. The core idea of the Monte Carlo principle is: using the simulation sampling results of a large amount of data to approximate the real physical process corresponding to the simulation model; on the premise that the simulation model is accurate, according to the law of large numbers, when the number of simulation samples is large enough, the obtained simulation results can infinitely approximate the real results.

[0047] Although the following embodiments of the present invention are also based on photon simulation, the focus is on photon counting, that is, after a number of photons go through a complex propagation process, how many photons are received by the detector, which belongs to the "counting problem". The following embodiments of the present invention take the light reflection model as the photon reflection principle and consider more about the three-dimensional space parameters of photons, including three-dimensional coordinates and flight direction vectors.

[0048] The following embodiments of the present invention solve the following technical problems:

[0049] 1. When single-pixel imaging is applied to three-dimensional objects, additional data components caused by the three-dimensional topography are introduced into the measurement data of the photodetector;

[0050] 2. In the single-pixel imaging simulation algorithm at the pixel level, it is difficult to complete the simulation calculation of such problems.

[0051] As Figure 1a 、 1b shown, the specific operation of Monte Carlo simulation is as follows: from the perspective of probability statistics, use the probability distribution model to perform the characterization operation of the probability density function for each stage in a specific physical system or physical process; after establishing the above probability model, determine the smallest research element in the simulation model; then initialize the attribute parameters of the research element by means of random number generation, and finally simulate the change of the attribute parameters of the research element in the whole physical process to obtain the final simulation result. Among them Figure 1a is the real physical process, Figure 1b is the simulation process.

[0052] And this simulation method is not applicable to all situations and needs to meet the following conditions: the research element object conforms to the corresponding probability distribution model. We find that for the SPI technology, its physical imaging process perfectly fits the Monte Carlo simulation conditions. Figure 5 is the schematic diagram of the imaging system device of SPI.

[0053] The laser light source used in single-pixel imaging belongs to a coherent light source. The monochromatic light beam it excites is used for spatial modulation of the backend optical path. Before that, this monochromatic uniform light beam is physically considered to be an approximate coherent light beam, and the photon radiation in the coherent light beam is the result of a single independent radiation process, which indicates that the number of its photons is a random process with a Poisson distribution. Under the condition of stable laser light source power, assuming that the number of photons emitted within the unit time Δt is k, and N is the average number of photons, and its value is determined by the physical parameters of the laser itself (fixed for a certain laser), it satisfies the following Poisson formula:

[0054]

[0055] Among them, p N (k) is the probability value when the excitation photon is k. Figure 2 is the probability distribution diagram where the number of excitation photons follows a Poisson distribution.

[0056] One of the core technologies of single-pixel imaging based on digital micromirror devices (DMD) lies in achieving different digital matrices by controlling the flipping of the micromirror array of DMD. At the mathematical level, it is represented as a 0-1 matrix, and at the microscopic photon level, it is represented as whether a photon is successfully reflected, corresponding to two states of photon survival or loss. According to the gating principle of DMD, the probability distribution of photons passing through DMD is defined as:

[0057]

[0058] According to the single-pixel imaging system, when a photon passes through the projection lens, the corresponding lens PSF function is used to simulate its propagation trajectory. In the photon propagation medium, assuming its one-way transmittance coefficient for photons is σ, which represents the probability of a photon successfully passing through the propagation medium as σ. The innovation of this invention lies in endowing the photon with three-dimensional coordinate attribute parameters (x i , y i , z i ) during the entire propagation process. According to the three-dimensional coordinates (x i0 , y i0 , z i0 ) and the flight direction vector (t x , t y , t z ) of the photon when it exits at the projection end, then use the iterative algorithm to calculate its flight landing point (x i-end , y i-end , z i-end ) on the target surface, and define the target surface reflection coefficient of this point as R(x i-end , y i-end , z i-end ). Its principle is as shown in Figure 4 .

[0059] In this step, the iterative algorithm used is the Newton iterative algorithm, which is specifically as follows:

[0060] As shown in Figure 6 , through successive iterations: 1→2→3→4→5→6……, keep iterating until the error is less than a set threshold. Finally, a photon landing point that meets the accuracy requirements is calculated, that is, the landing point of a flying photon on the target (knowing its flight direction vector and three-dimensional coordinates). For the detailed algorithm logic, refer to the Newton iterative algorithm.

[0061] It should be noted that the target surface reflectance follows a unified reflection theory model (the Phong model with wide applicability is adopted in the present invention), and its value is affected by: the photon incident angle, the detector receiving angle, the normal vector, and the material characteristics of the target itself. The above model formula is as follows:

[0062] R = r a + k s r s + k d r d ·cosθ (3)

[0063] Among them, r a is the environmental error term, k s r s is the diffuse reflection term, k d r d is the specular reflection term, and θ is the angle between the outgoing direction and the normal.

[0064] According to the reflectance of the target surface, when a photon hits a certain point, the probability of its being reflected is equal to its reflectance R(x i-end , y i-end , z i-end ). If all the surviving photons are considered (assuming the number of surviving photons at this time is N s ), then the number of photons received by the detector follows a binomial distribution:

[0065] (4)

[0067] Among them, P(X = n) is the probability of receiving n photons. Assuming that the total number of photons received by the detector is N d , and its photoelectric conversion efficiency coefficient is η, then the magnitude of the final simulated voltage signal is ηN d .

[0068] 1.2 Establish a simulation module to implement the photon state at each stage in the simulated three-dimensional single-pixel imaging

[0069] For the probability model and simulation process constructed above in the present invention, data simulation is carried out in the form of a computer program module to implement a complete simulation system for three-dimensional single-pixel imaging photon counting based on the Monte Carlo principle.

[0070] The following table is an example of a pseudocode module:

[0071]

[0072]

[0073] Such as Figure 7, the pseudo-code module process of this Monte Carlo simulation algorithm is as follows:

[0074] Input: Imaging environment definition (imaging distance, projection angle, instrument three-dimensional coordinates, noise parameters, attenuation coefficient of the propagation medium, coding pattern diagram), target object definition (surface reflectivity of the target object, 3D topography parameters) Output: Photoelectric signal sequence values of the single-pixel detector

[0075] Algorithm process:

[0076] 1. Input loading and parameter initialization settings.

[0077] 2. Traverse each frame of the coding pattern diagram:

[0078] (a). Photon excitation and coding pattern diagram loading: Generate a photon group whose quantity follows a Poisson distribution; (b). Spatial light modulator encodes the photon distribution: Determine whether the photons are successfully reflected through the micromirror array; (c). Photon flight calculation: Calculate the landing position of the surviving photons on the target object surface through an iterative algorithm;

[0079] (d). Photon counting: Calculate whether the photons are received according to the reflectivity at the landing point and the detector receiving position.

[0080] 3. Output the final result: Photoelectric signal sequence values.

[0081] Among them, the above-mentioned photon flight landing point calculation module is one of the innovation points of the present invention. This module analyzes the spatial position change of photons in the three-dimensional coordinate system and the change of their flight direction vectors.

[0082] In the photon flight landing point calculation module, a probability distribution model is used to perform the characterization operation of the probability density function for each stage in a specific physical system or physical process; after establishing the above probability model, determine the smallest research element in the simulation model; then initialize the attribute parameters of the research element by means of random number generation, and finally simulate the change of the attribute parameters of the research element in the whole physical process to obtain the final simulation result.

[0083] Experimental example

[0084] This technology is applicable to the simulation of the photoelectric signal values received by the detector and does not involve the backend reconstruction algorithm. And the reconstruction algorithm is closely related to the measured photoelectric signal, so the feasibility of the invention can be illustrated by comparing the photoelectric signal values of the two.

[0085] Apply the photon counting simulation method proposed in the present invention to the SPI system we built. First, use a set of specified coding pattern diagrams to image real three-dimensional objects (including: planar targets and three-dimensional target standards), obtaining the corresponding optoelectronic signal sequence values. Then, use the same coding pattern diagrams to complete the corresponding simulation calculations in a simulation environment respectively, and compare the parameters with the signals collected in the actual scenario. Among them, the photon simulation uses MATLAB2020a in a 64-bit Windows 10 operating system with 16G of RAM as the test platform, and the results such as Figure 3 can be obtained. Among them, 4 is the real sampling signal: planar target, 5 is the real sampling signal: three-dimensional target, 6 is the simulation signal: planar target, and 7 is the simulation signal: three-dimensional target.

[0086] Through the above data simulation and experimental analysis, we use the Pearson correlation coefficient (a linear evaluation parameter index) to evaluate the data, as described in Table 1.

[0087] Table 1 - Parameter Evaluation of Pearson Correlation Coefficient

[0088]

[0089]

[0090] It can be seen that: for the algorithm proposed in the embodiment of the present invention when facing planar targets and three-dimensional targets, the correlation coefficients between the simulated simulation numerical results and the real sampling signals are all greater than 0.85. In probability statistics, when the correlation coefficient is greater than 0.8, it is considered that the two are highly correlated, while other correlation coefficients are all lower than 0.7, and the data difference represents the 3D shape information contained in the three-dimensional target.

[0091] The above embodiments of the present invention have great development potential, such as:

[0092] 1. This technology can be applied to three-dimensional single-pixel imaging and auxiliary imaging in the future;

[0093] 2. This technology can also be combined with deep learning to improve the accuracy of three-dimensional imaging.

[0094] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0095] The present invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each flow and / or block in the flowchart illustrations and / or block diagrams, and combinations of flows and / or blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing apparatus create means for implementing the functions specified in one or more flows of the flowchart and / or one or more blocks of the block diagram.

[0096] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means that implement the functions specified in one or more flows of the flowchart and / or one or more blocks of the block diagram.

[0097] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more flows of the flowchart and / or one or more blocks of the block diagram.

[0098] The above content is a further detailed description of the present invention in combination with specific / preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several alternatives or modifications can be made to these described embodiments, and these alternative or modified forms should all be regarded as belonging to the protection scope of the present invention. In the description of this specification, the description with reference to terms such as "an embodiment", "some embodiments", "preferred embodiments", "examples", "specific examples" or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. Without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the protection scope of the invention application.

Claims

1. A photon counting simulation method for three-dimensional single-pixel imaging, characterized in that, Including the following steps: Using a specified coding pattern diagram, perform corresponding simulation calculations in a simulation environment respectively: From the perspective of photons, with photons as the basic simulation unit, conduct three-dimensional single-pixel imaging photon counting simulation based on the Monte Carlo principle, and establish a simulation module to realize the photon states at each stage in the simulated three-dimensional single-pixel imaging; The algorithm of the said simulation module includes the following steps: S1: Input loading and parameter initialization settings; S2: Traverse each frame of the coding pattern diagram; Step S2 includes the following steps: S2-1: Photon excitation and coding pattern diagram loading: Generate a photon group whose quantity follows a Poisson distribution; S2-2: Spatial light modulator encodes the photon distribution: Judge whether the photons are smoothly reflected through the micromirror array; S2-3: Photon flight calculation: Calculate the landing position of the surviving photons on the target surface through an iterative algorithm; S2-4: Photon counting: Calculate whether the photons are received according to the reflectivity at the landing point and the detector receiving position; In step S2-3, the said photon flight calculation includes the following steps: S2-3-1: When the photons pass through the projection lens, use the corresponding lens PSF function set to simulate their propagation trajectory; S2-3-2: In the photon propagation medium, assuming that the one-way transmission coefficient of the photon is σ, which represents the probability of the photon passing through the propagation medium smoothly as σ, assign the three-dimensional coordinate attribute parameters (x i , y i , z i ) to the photon during the entire propagation process. According to the three-dimensional coordinates (x i0 , y i0 , z i0 ) and the flight direction vector (t x , t y , t z ) of the photon when it exits at the projection end, then use the iterative algorithm to calculate its flight landing point (x i-end , y i-end , z i-end ) on the surface of the target object.

2. The photon counting simulation method for three-dimensional single-pixel imaging according to claim 1, characterized in that, The input of the said simulation module is: imaging environment definition and target definition, where the imaging environment definition includes imaging distance, projection angle, instrument three-dimensional coordinates, noise parameters, attenuation coefficient of the propagation medium, coding pattern diagram; the target definition includes the surface reflection coefficient of the target and 3D topography parameters.

3. The photon counting simulation method for three-dimensional single-pixel imaging according to claim 1, characterized in that, The output of the said simulation module is the sequence value of the optoelectronic signal of the single-pixel detector.

4. The photon counting simulation method for three-dimensional single-pixel imaging according to claim 1, characterized in that, The said iterative algorithm is the Newton iterative algorithm.

5. The photon counting simulation method for three-dimensional single-pixel imaging according to claim 1, wherein Define the surface reflection coefficient at the flight landing point on the surface of the target as R(x i-end , y i-end , z i-end ), Then R = r a + k s r s + k d r d · cos θ Among them, r a is the environmental error term, k s r s is the diffuse reflection term, k d r d is the specular reflection term, θ is the angle between the outgoing direction and the normal, x i-end , y i-end , z i-end represent the coordinates of the landing point.

6. The photon counting simulation method for three-dimensional single-pixel imaging according to claim 1, characterized in that This method can also be combined with deep learning to improve the accuracy of three-dimensional imaging.

7. A photon counting simulation device for three-dimensional single-pixel imaging, on which a computer program is stored, characterized in that, When this computer program is executed by a processor, it can implement the photon counting simulation method for three-dimensional single-pixel imaging described in any one of claims 1-6.

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