CN112540381A - Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform - Google Patents

Abstract

The invention discloses a non-visual field single-input multiple-output three-dimensional reconstruction method of non-uniform fast Fourier transform. The single-in-multiple-out technology was introduced for the first time in the field of non-view-of-sight imaging, and the non-uniform fast Fourier transform was used to perform fast imaging of non-view-of-sight scenes by using the existing system. It includes the following steps: using a laser to non-uniformly scan the reflective intermediate surface, and using a detector to receive a time-photon histogram of echoes, preprocessing the received data, and converting the received time-photon data into time-amplitude data; for The preprocessed data uses an optimization algorithm to solve the optimal time-wavenumber spectrum through the two-dimensional non-uniform fast Fourier transform relationship in the space dimension, and then performs a one-dimensional fast Fourier transform on the time dimension on the time-wavenumber spectrum; The single-input multiple-output frequency domain algorithm is used to interpolate the transformed spectrum; the inverse fast Fourier transform is performed on the interpolated spectrum to obtain the 3D reconstruction result of the non-view domain scene.

Description

Non-Horizons Single-In-Multiple-Out 3D Reconstruction Method Based on Non-Uniform Fast Fourier Transform

technical field

The invention belongs to the field of laser non-visual field imaging, and in particular relates to a non-visual field three-dimensional reconstruction method based on non-uniform fast Fourier transform and single-in-multiple-out technology.

Background technique

In recent years, non-horizontal imaging technology has developed rapidly. It is a new imaging technology for 2D or 3D reconstruction of scenes outside the observer's visible area. It has a good development in complex area detection, vehicle driving assistance, and medical imaging. Foreground; non-horizontal imaging mainly uses the time-of-flight data of the secondary echoes of the detection area of interest to reconstruct the hidden target object.

The development of non-horizontal imaging has gone through several stages. From Kirmani et al. first proposed the concept of time-of-flight to recover hidden objects, Velten et al. used a streak camera as a detector, and used a filtered back-projection algorithm to demonstrate the 3D non-horizontal scene for the first time. According to the experimental reconstruction results, Buttafava et al. used the single-photon avalanche diode as the detector for non-horizontal reconstruction. These early non-horizontal imaging algorithms depended on non-confocal system implementation, and the computational complexity was too high O(N ⁵ ), The reconstruction accuracy is not high.

Until 2018, O'toole et al. improved the imaging system to confocal mode, and proposed a light cone transformation algorithm to obtain higher-precision reconstruction, and the algorithm complexity was reduced to O(N ³ logN); Lindell et al. In the confocal system, the frequency wavenumber (fk) algorithm of seismic waves is introduced, and the algorithm complexity is also O(N ³ logN), and high-precision reconstruction is obtained; in addition, Liu et al. Perform higher-precision reconstructions.

The so-called "confocal system" means that the receiving optical path of the detector is the same as the transmitting optical path of the laser during the imaging process, and the laser irradiation point is juxtaposed with the receiving point of the detector; the introduction of the confocal system simplifies the imaging optical path, which in turn simplifies the model. In the imaging process, the receiving optical path of the detector is the same as the transmitting optical path of the laser, which is generally realized by a beam splitter, but there are the following problems: the received energy is obviously attenuated; the optical path design is complicated; because the direct echo energy is often significantly larger than the two containing the reconstructed target data. The secondary echo energy, confocal design will make this phenomenon more obvious, which will interfere with the measurement data.

SUMMARY OF THE INVENTION

In view of the existing non-visual field imaging algorithms, which rely on non-confocal systems to implement, there are problems such as high computational complexity and low reconstruction accuracy, and relying on confocal systems to implement, the existing optical path design is complex, and the measurement data is susceptible to secondary echoes Energy interference and other problems, the present invention provides a non-visual field single-in-multiple-out three-dimensional reconstruction method based on non-uniform fast Fourier transform, which can utilize non-confocal system for high-precision simple and fast reconstruction of non-visual field scenes.

The technical solution of the present invention is to provide a non-view-domain single-in-multiple-out three-dimensional reconstruction method based on non-uniform fast Fourier transform, which is special in that it includes the following steps:

Step 1, data preprocessing;

并用探测器单点接收回波的时间-光子直方图数据，设定x_R为接收点XOY空间坐标，对时间-光子直方图数据预处理，将其转化为时间-幅值数据{θ_j[t]}_j＝0:M-1；其中，x_T为扫描点XOY空间坐标，{.}_j＝0:M-1表示M个元素构成的集合,元素下标j表示第j个扫描点(x_T)_j对应的数据；由于扫描点个数为M，j的取值范围为0至M-1的整数；The multi-point non-uniform laser scanning of the reflection intermediate surface is used, and the number of scanning points is M, and the multi-point non-uniform scanning coordinate set is obtained.

And use the time-photon histogram data of the echo received by the detector at a single point, set x _R as the XOY space coordinate of the receiving point, preprocess the time-photon histogram data, and convert it into time-amplitude data {θ _j [ t]} _j=0:M-1 ; wherein, x _T is the XOY space coordinate of the scanning point, {.} _j=0:M-1 represents the set formed by M elements, and the element subscript j represents the jth scanning point (x _T ) data corresponding to _j ; since the number of scanning points is M, the value range of j is an integer from 0 to M-1;

Step 2. Use an optimization algorithm for the preprocessed data to solve the optimal time-wavenumber spectrum through the two-dimensional non-uniform fast Fourier transform relationship of the space dimension, and then perform a one-dimensional time dimension on the optimal time-wavenumber spectrum. Fast Fourier transform to obtain the optimal frequency-wavenumber spectrum;

Step 2.1. For the time-amplitude data {θ _j [t]} _j=0:M-1 obtained in step 1, set the reconstruction spatial resolution, and scan the coordinate set χ and the time-amplitude data {θ _j [ t]} _j=0:M-1 , obtain the two-dimensional non-uniform fast Fourier transform relationship in the spatial dimension, and the corresponding matrix operators V, F, S; solve the optimal time-wavenumber spectrum Φ[t, k _x , k _y ], to minimize the difference between the optimal time-wavenumber spectrum and the real time-wavenumber spectrum; where t represents time, and k _x and _ky represent the two-dimensional XOY space on the X and Y dimensions, respectively. wave number;

Step 2.2. Use the optimal time-wavenumber spectrum Φ[t,k _x ,k _y ] transformed in step 2.1 to perform one-dimensional fast Fourier transform in the time dimension to obtain the optimal frequency-wavenumber spectrum Φ[f,k _x , k _y ], where f represents the frequency in the time dimension;

Step 3. Interpolate the optimal frequency-wavenumber spectrum Φ[f, k _x , _ky ] using the single-input multiple-output frequency domain algorithm, and obtain the spectrum Ψ[k _z , k _x , _ky ] after compensation; where k _z represents the wave number in the Z-axis direction;

Step 3.1. Use the frequency-wavenumber relationship derived from the dispersion relationship to perform interpolation calculation on the optimal frequency-wavenumber spectrum Φ[f, k _x , k _y ] using the single-input multiple-output method to obtain the spectrum after the interpolation calculation

添加补偿项，进行相位补偿，获得相位补偿后的频谱Ψ[k_z，k_x，k_y]；Step 3.2, the spectrum after interpolation calculation

Add a compensation term, perform phase compensation, and obtain the phase-compensated spectrum Ψ[k _z , k _x , _ky ];

Step 4. Perform an inverse fast Fourier transform on the phase-compensated spectrum Ψ[k _z , k _x , _ky ] to obtain a three-dimensional reconstruction result of the non-view domain scene.

Further, in step 3.1:

In step 3.2:

In the formula, Z ₀ represents the Z-coordinate position of the reflection intermediate surface.

Further, step 1 specifically includes:

Step 1.1. Set the world coordinate system; among them, the XOY plane coincides with the reflection intermediate plane, the Z axis is perpendicular to the XOY plane, and the positive direction of the Z axis points to the non-view field scene;

其中，(x_T)_j为第j个扫描点XOY空间坐标；设置接收点空间坐标x_R，处于扫描区域的中心；Step 1.2. Set the multi-point non-uniform scanning coordinates of the laser to obtain a multi-point non-uniform scanning coordinate set

Wherein, (x _T ) _j is the XOY spatial coordinate of the jth scanning point; set the spatial coordinate x _R of the receiving point, which is in the center of the scanning area;

Step 1.3, for different scanning points, the detector accumulatively receives the corresponding time-photon histogram data set {τ _j [t]} _j=0:M-1 ;

Among them, {.} _j=0:M-1 represents a set composed of M elements, and the element subscript j represents the data corresponding to the jth scan point (x _T ) _j . Since the number of scan points is M, the value of j The value range is an integer from 0 to M-1; τ _j [t] represents the number of photons received by the detector at the j-th scanning point, namely (x _T ) _j , at time t, which is used to compare with the number of photons received by the detector. The time-photon histogram corresponds to the data; the subscript T represents the scanning point, which corresponds to the subscript R of the receiving point;

Step 1.4, preprocessing the time-photon histogram data set;

In the formula, θ _j [t] represents the time-amplitude data of the corresponding scanning point (x _T ) _j at time t.

Further, in step 2.1, the two-dimensional non-uniform fast Fourier transform in the spatial dimension is obtained by the following formula:

表示空间维度上的二维伴随非均匀快速傅里叶变换；Θ[t,k_x，k_y]为非均匀快速傅里叶变换后的时间-波数谱；In the formula,

represents the two-dimensional adjoint non-uniform fast Fourier transform in the spatial dimension; Θ[t,k _x , k _y ] is the time-wavenumber spectrum after the non-uniform fast Fourier transform;

The matrixed expression of the above formula:

Θ=S ^H F ^H V ^H θ

V, F, S are the matrix operators corresponding to the non-uniform fast Fourier transform, V is the interpolation matrix; F is the fast Fourier transform matrix; S is the up-sampling matrix; H is the Hermitian transpose of the matrix;

Using the conjugate gradient optimization algorithm to solve the optimal time-wavenumber spectrum Φ, namely Φ[t,k _x ,k _y ], the objective formula is as follows:

表示

的最优化估计，

是

的矩阵化表示，

与最优时间-波数Φ有如下关系：

express

The optimal estimate of ,

Yes

The matrix representation of ,

It is related to the optimal time-wave number Φ as follows:

where S ⁺ represents the inverse or pseudo-inverse of the matrix S.

The beneficial effects of the present invention are:

1. The present invention compares the similarity between the synthetic aperture radar model and the non-visual field model, introduces the non-visual field reconstruction into the characteristics of the virtual wave, introduces the single-in-multiple-out algorithm into a new field, and performs non-visual field imaging calculation through For the interpolation processing in the frequency domain of the measurement data, the complicated and cumbersome back-projection reconstruction is avoided, which greatly improves the imaging rate and accuracy; because the non-view field is in its infancy, there is no general means to improve the imaging rate; and the means to improve the accuracy are relatively Single, it is common to perform three-dimensional Laplace filtering on the reconstructed result, but the present invention can obtain a clear imaging result without this filtering operation.

2. The present invention can be implemented based on a non-confocal system, and does not depend on the design of a confocal imaging system, which improves the flexibility of imaging.

3. The present invention uses the non-uniform Fourier transform and the corresponding conjugate gradient algorithm, and can use the down-sampled non-uniform data to quickly and effectively restore the frequency spectrum close to the real data; it can significantly reduce the number of scanning points, reduce The time the algorithm collects data.

4. The present invention utilizes the non-uniform Fourier transform and the corresponding conjugate gradient algorithm, which can focus on collecting the region of interest, obtain non-uniform data after focusing on collecting the region of interest, fully obtain the data information of the region of interest, and further improve the imaging flexibility . However, the existing non-horizontal imaging algorithms have the shortcomings of slow imaging speed (such as filtered back projection algorithm, virtual wave algorithm) or relying on uniform data (such as light cone transformation algorithm, frequency wavenumber (f-k) algorithm of confocal system), It is difficult to balance the imaging speed and the data sampling method.

Description of drawings

FIG. 1 is a schematic diagram of a non-confocal system according to an embodiment of the present invention.

FIG. 2 is a flowchart of a non-view domain single-input multiple-output three-dimensional reconstruction method provided by a non-uniform fast Fourier transform according to the present invention.

FIG. 3 is a comparison diagram of part of the time-space data after inverse Fourier transform of the spectrum obtained by optimization and original data in an embodiment of the present invention.

FIG. 4 is a schematic diagram of a non-field of view imaging result according to an embodiment of the present invention.

The reference numbers in the figure are: 1-pulse laser, 2-single photon detector SPAD, 3-time correlation counting module TCSPC, 4-reflection intermediate surface, 5-target object, 6-scanning system.

Detailed ways

The present invention will be further described below through the accompanying drawings and specific embodiments. The following embodiments are intended to be used to explain the present invention, but should not be construed as limitations of the present invention; it should be noted that, for the convenience of description, the accompanying drawings only show The embodiments of the present application and the features of the embodiments can be combined with each other without conflicting with the parts related to the related invention.

A non-visual field imaging algorithm of the present invention is used for fast and high-precision imaging of a laser non-confocal system;

1 is a non-field of view imaging system elements included in a laser non-confocal system provided by an embodiment of the present invention: a pulsed laser 1, a single-photon detector SPAD2, a time-correlated counting module TCSPC3, a reflection intermediate surface 4, and a target object 5 and scanning system 6; wherein the laser emits pulse signals of equal energy at high frequency to illuminate the designated position point on the reflection intermediate surface 4 through the scanning system 6 and the emission optical system; the reflection intermediate surface is generally a diffuse reflector, which produces the first The secondary diffuse reflection illuminates the target object 5; the target object 5 is facing the scanning area, receives the photon signal reflected for the first time, and generates the second reflection; the photon signal reflected by the second time is returned to the reflection intermediate surface, and The third reflection is generated on the intermediate surface; the single-photon detector SPAD2 adopts the gating mode and only accepts the photon signal from the third reflection, that is, the so-called second echo data; through accumulation, the time-correlated counting module TCSPC3 is used , which generates a time-photon histogram of the echoes.

2 is a flowchart of a method for reconstructing a non-view 3D scene based on a non-confocal system non-uniform fast Fourier transform provided by an embodiment of the present invention, including the following steps:

Step 1: Use the laser to non-uniformly scan the reflection intermediate surface at multiple points, and use the detector to receive the time-photon histogram of the echo at a single point, preprocess the received data, and convert the received time-photon data into time-amplitude Data; in Figure 1, "×" represents the laser scanning point, and "●" represents the detector receiving point.

1.1), set the XYZ world coordinate system; in which, the XOY plane coincides with the reflection intermediate plane, the Z axis is perpendicular to the XOY plane, and the positive direction of the Z axis points to the non-view field scene;

采样自XOY二维空间

设置探测器接收点坐标

x_T为扫描点XOY空间坐标；x_R为接收点XOY空间坐标，处于扫描区域的中心，x_R＝(0,0)；1.2), set the multi-point non-uniform scanning coordinate set of the laser

Sampling from XOY two-dimensional space

Set the coordinates of the detector receiving point

x _T is the XOY space coordinate of the scanning point; x _R is the XOY space coordinate of the receiving point, which is in the center of the scanning area, x _R =(0,0);

1.3) For different scanning points, the receiver receives and accumulates to obtain the corresponding time-photon histogram set, which is recorded as:

T:={τ _j [t]} _j=0:M-1

In the formula, τ _j [t] represents the number of photons received by the detector when the scanning point is at (x _T ) _j , time t, which is regarded as a function of time t; for each histogram τ _j [t], Time t=0 corresponds to the time when the laser pulse reaches the scanning point (x _T ) _j for the first time; wherein, the length on the time dimension t is N _t ;

1.4), perform preprocessing for each histogram data, as follows:

Specifically, before the laser is used for scanning, a non-uniform scanning mode is set in advance, the number of scanning points is M, and their positions can be random or designed; the received data is the "time-photon number" data, which is also It is the "time-intensity" data, so the received data should be preprocessed to become "time-amplitude" data, which is regarded as a kind of virtual wave.

Step 2: Perform a two-dimensional non-uniform fast Fourier transform in the spatial dimension and a one-dimensional fast Fourier transform in the time dimension on the data preprocessed in the first step, including:

2.1), set the reconstruction spatial resolution, use the multi-point non-uniform scanning coordinate set χ and the processed data in step 1.4 {θ _j [t]} _j=0:M-1 to obtain the two-dimensional non-uniformity in the spatial dimension. The fast Fourier transform corresponds to the matrix operators V, F, and S, and the conjugate gradient optimization algorithm is used to solve the optimal time-wavenumber spectrum Φ[t,k _x ,k _y ] uniformly distributed on the space dimension Cartesian coordinate system;

The two-dimensional non-uniform fast Fourier transform relationship in the spatial dimension is:

表示空间维度的二维伴随非均匀快速傅里叶变换；Θ[t，k_x，k_y]表示非均匀快速傅里叶变换后得到的时间-波数谱；其中t表示时间，k_x、k_y表示二维XOY空间分别在X、Y维度上的波数；In the formula,

Represents the two-dimensional adjoint non-uniform fast Fourier transform of the spatial dimension; Θ[t, k _x , k _y ] represents the time-wavenumber spectrum obtained after the non-uniform fast Fourier transform; where t represents time, k _x , k _y represents the wavenumber of the two-dimensional XOY space in the X and Y dimensions respectively;

表示空间维度的二维伴随非均匀快速傅里叶变换，是二维非均匀快速傅里叶变换的逆过程；in,

The two-dimensional adjoint non-uniform fast Fourier transform representing the spatial dimension is the inverse process of the two-dimensional non-uniform fast Fourier transform;

Two-dimensional non-uniform fast Fourier transform is used to solve the problem of Fourier transform from uniform data to non-uniform data. Fast Fourier transform is performed on the smoothed sample data; the interpolation step removes the influence of the basis function on the transform result. The above process relationship can be expressed as a combination of matrixed linear operations:

Θ=VFSΘ

In the formula, V is the interpolation matrix; F is the fast Fourier transform matrix; S is the up-sampling matrix; θ is the vectorized representation of {θ _j [t]} _j=0:M-1 ; Θ is Θ[t, The matrix representation of k _x , k _y ]; the above formula expresses that the data set {θ _j [t]} _j=0:M-1 obtained from the spatially non-uniform scanning point χ can be considered as a uniform time-wavenumber spectrum Θ[t, k _x , _ky ] is obtained by two-dimensional non-uniform fast Fourier transform according to the non-uniform scanning point χ.

The two-dimensional accompanying non-uniform fast Fourier transform is the inverse process of the two-dimensional non-uniform fast Fourier transform. It is used to solve the problem of Fourier transform from non-uniform data to uniform data. The process can also be expressed as a matrix Combination of linearized operations:

Θ=S ^H F ^H V ^H θ

The above formula is the process of obtaining the uniform time-wavenumber spectrum Θ[t, k _x , k _y ] by using the data set {θ _j [t]} _j=0:M-1 using the two-dimensional adjoint non-uniform fast Fourier transform to solve ; The H in the upper right corner of the matrix symbol represents the Hermitian transpose of the matrix.

However, due to the incompleteness of the data obtained from the non-uniform scanning points, especially when down-sampling reconstruction, the result of directly using the accompanying non-uniform fast Fourier transform is not ideal. Therefore, the result Θ (ie, Θ[t, k _x , k _y ]) of the accompanying non-uniform fast Fourier transform is generally not directly used, and the non-uniform Fourier transform relationship is usually used to solve the real The optimal time-wavenumber spectrum Φ[t,k _x , _ky ] that minimizes the difference between the spectra; the matrix of the optimal reconstructed time-wavenumber spectrum Φ[t,k _x , _ky ] is expressed as Φ, The objective formula is solved by the conjugate gradient algorithm as follows:

表示

的最优化估计，

是

的矩阵化表示，是计算过程的中间变量，

与求解估计的最优时间-波数Φ有如下关系：

express

The optimal estimate of ,

Yes

The matrix representation of , is the intermediate variable of the calculation process,

It is related to the optimal time-wavenumber Φ for solving the estimation as follows:

In the formula, S ⁺ represents the inverse or pseudo-inverse of the matrix S;

2.2), perform a one-dimensional fast Fourier transform in the time dimension for the optimal time-wavenumber spectrum Φ[t,k _x , _ky ]:

表示时间维度t上的一维快速傅里叶变换；其中f表示时间维度上的频率；In the formula,

represents the one-dimensional fast Fourier transform in the time dimension t; where f represents the frequency in the time dimension;

Step 3: Interpolate the transformed spectrum by using the single-in-multiple-out technology:

与测量数据频率-波数谱Φ[k_z,k_x,k_y]的映射关系：3.1) Reconstructing the 3D wavenumber spectrum

Mapping relationship with measured data frequency-wavenumber spectrum Φ[k _z ,k _x ,k _y ]:

k_z表示Z轴方向上的波数；The mapping relationship of the above formula is obtained by the single-input multiple-output frequency domain algorithm, and the reconstructed spectrum uniformly distributed in the wavenumber space obtained by interpolation according to the above mapping relationship

k _z represents the wave number in the Z-axis direction;

3.2) Add a compensation item to perform phase compensation:

In the formula, Z ₀ represents the Z-axis coordinate position of the reflection intermediate surface; Ψ represents the spectral data after adding the compensation term;

重建三维波数谱

与测量数据频率-波数谱Φ的映射关系

由上述关系推导而得；由重建三维波数谱

与测量数据频率-波数谱Φ的映射关系可知，所需要的频率-波数谱Φ的值，通过

而得，所需频率f在笛卡尔坐标系上并非均匀分布，因而要通过插值计算得到；Specifically, the frequency-wavenumber relationship in the non-confocal case derived from the dispersion relationship:

Reconstructed 3D wavenumber spectrum

Mapping relationship with measured data frequency-wavenumber spectrum Φ

is derived from the above relationship; from the reconstructed three-dimensional wavenumber spectrum

The mapping relationship with the frequency-wavenumber spectrum Φ of the measured data shows that the required value of the frequency-wavenumber spectrum Φ can be obtained by

Therefore, the required frequency f is not uniformly distributed in the Cartesian coordinate system, so it needs to be calculated by interpolation;

Step 4: Perform an inverse fast Fourier transform on the interpolated spectrum to obtain a three-dimensional reconstruction result of the non-view field scene:

4.1) Inverse Fourier Transform Transform:

In the formula, ψ three-dimensional represents the spatial domain data obtained after inverse Fourier transform;

4.2) Obtain the non-view reconstruction result |ψ(z, x, y)| ²

The present invention will be further described below with reference to specific embodiments.

Step 1: Using the imaging system shown in Figure 1, the laser is used to non-uniformly scan the reflection intermediate surface, and the scanning point is randomly selected to scan, the number of scanning points is M=2000, and the time-photon histogram of the echo is received by the detector, Preprocess the received data, convert the received time-photon data into time-amplitude data; set the reconstruction target as Stanford Rabbit;

Step 2: Perform a one-dimensional fast Fourier transform in the time dimension and a two-dimensional non-uniform fast Fourier transform in the space dimension on the preprocessed data, and set the wavenumber domain resolution of the non-uniform fast Fourier transform to 256× 256, the resolution of the final reconstructed and restored data image is 128×128, that is, the sampling rate is 12.2%; the conjugate gradient optimization algorithm is used to solve the optimal time-wavenumber spectrum uniformly distributed on the space dimension Cartesian coordinate system; - After the two-dimensional inverse Fourier transform of the wavenumber spectrum, the obtained part of the time-space data is compared with the original data as shown in Figure 3. It can be seen that the echo data is obviously complemented, and the details of the echo shape, trend, energy distribution, etc. Compared with the previous one, it is obviously improved; the fast Fourier transform of the time dimension is performed on the time-wavenumber spectrum, and finally the frequency-wavenumber spectrum for step 3 is obtained;

Step 3, using the single-input multiple-output technology to perform interpolation processing on the transformed spectrum;

Step 4: Perform inverse fast Fourier transform on the interpolated spectrum to obtain the 3D reconstruction result of the non-view field scene; In the area with better reflection conditions, such as the rabbit thigh near the reflection intermediate surface, the reconstruction result is fine; in the area with poor reflection conditions, such as the rabbit ear far away from the reflection intermediate surface, the reconstruction result still has the corresponding contour .

The above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation method of the present invention. For those of ordinary skill in the art, changes or modifications in other different forms can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. Any modifications, equivalent replacements and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (4)

1. A non-visual field single-input multi-output three-dimensional reconstruction method based on non-uniform fast Fourier transform is characterized by comprising the following steps:

step 1, preprocessing data;

adopting a laser multi-point non-uniform scanning reflection interface, wherein the number of scanning points is M, and obtaining a multi-point non-uniform scanning coordinate set

And using a single point of the detector to receive the time-photon histogram data of the echo, setting x_RFor the XOY space coordinate of the receiving point, the time-photon histogram data is preprocessed and converted into time-amplitude data { theta [ theta ])_j[t]}_j＝0：M-1(ii) a Wherein x is_TIs the space coordinate of the scanning point XOY { }_j＝0：M-1Representing a set of M elements, the element index j representing the j-th scan point (x)_T)_jCorresponding data;

step 2, solving an optimal time-wave number spectrum by utilizing an optimization algorithm for the preprocessed data through a two-dimensional non-uniform fast Fourier transform relation of a space dimension, and then performing one-dimensional fast Fourier transform on the optimal time-wave number spectrum in a time dimension to obtain an optimal frequency-wave number spectrum;

step 2.1, for the time-amplitude data { θ ] obtained in step 1_j[t]}_j＝0：M-1Setting the resolution of reconstruction space, and scanning coordinate set chi and time-amplitude data theta_j[t]}_j＝0：M-1Obtaining a two-dimensional non-uniform fast fourier transform relationship in the spatial dimension and a corresponding matrixing operator V, F, S; solving for the optimal time-wavenumber spectrum phi t, k_x，k_y]Minimizing the difference between the optimal time-wavenumber spectrum and the true time-wavenumber spectrum; wherein t representsTime, k_x、k_yRepresenting wavenumbers in the X, Y dimensions of the two-dimensional XOY space, respectively;

step 2.2, adopting the optimal time-wave number spectrum phi [ t, k after the transformation in the step 2.1_x，k_y]Performing one-dimensional fast Fourier transform in time dimension to obtain optimal frequency-wave number spectrum phi [ f, k [ ]_x，k_y]Where f represents frequency in the time dimension;

step 3, utilizing a single-input multiple-output frequency domain algorithm to carry out optimal frequency-wave number spectrum phi [ f, k ]_x，k_y]Interpolation processing is carried out, and spectrum psi [ k ] is obtained after compensation_z，k_x，k_y](ii) a Wherein k is_zRepresents the wave number in the Z-axis direction;

step 3.1, using the frequency-wavenumber relationship deduced from the dispersion relationship and adopting a single-talk multi-output method to optimize the frequency-wavenumber spectrum phi [ f, k_x，k_y]Performing interpolation calculation to obtain spectrum after interpolation calculation

Step 3.2, spectrum after interpolation calculation

Adding compensation items to perform phase compensation to obtain a frequency spectrum psi [ k ] after phase compensation_z，k_x，k_y]；

Step 4, aiming at the frequency spectrum psi [ k ] after phase compensation_z，k_x，k_y]And performing inverse fast Fourier transform to obtain a non-view scene three-dimensional reconstruction result.

2. The non-uniform fast fourier transform based non-view single-in multiple-out three-dimensional reconstruction method according to claim 1, wherein:

step 3.1:

in step 3.2:

in the formula, Z₀Indicating the Z-axis coordinate position of the interface in reflection.

3. The non-field single-input multi-output three-dimensional reconstruction method based on the non-uniform fast fourier transform as claimed in claim 1 or 2, wherein the step 1 specifically comprises:

step 1.1, setting a world coordinate system; wherein the XOY plane is superposed with the reflective intermediate plane, the Z axis is vertical to the XOY plane, and the positive direction of the Z axis points to a non-visual field scene;

step 1.2, setting multi-point non-uniform scanning coordinates of the laser to obtain a multi-point non-uniform scanning coordinate set

Setting receiving point space coordinate x_RAt the center of the scanning area;

step 1.3, for different scanning points, the detector accumulatively receives to obtain a corresponding time-photon histogram data set { tau_j[t]}_j＝0：M-1；

Wherein, tau_j[t]Indicating that the scanning point is at the jth scanning point, namely (x)_T)_jAt time t, the number of photons received by the detector; wherein x is_TIs the space coordinate of the scanning point XOY; subscript T represents a scanning point, corresponding to subscript R of the reception point;

step 1.4, preprocessing a time-photon histogram data set;

in the formula, theta_j[t]Indicating the corresponding scanning point (x)_T)_jTime-amplitude data at time t.

4. The non-uniform fast fourier transform based non-view single-in multiple-out three-dimensional reconstruction method according to claim 3, wherein the two-dimensional non-uniform fast fourier transform in spatial dimension is obtained in step 2.1 by:

in the formula,

representing a two-dimensional adjoint non-uniform fast Fourier transform in a spatial dimension; theta [ t, k ]_x，k_y]Is a time-wave number spectrum after non-uniform fast Fourier transform;

the expression after matrixing by the above formula:

Θ＝S^HF^HV^Hθ

v, F, S is a non-uniform fast Fourier transform corresponding matrixing operator, V is an interpolation matrix; f represents a fast Fourier transform matrix; s is an upsampling matrix; h represents the hermite transpose of the matrix;

method for solving optimal time-wave number spectrum phi (phi t, k) by using conjugate gradient optimization algorithm_x，k_y]The solution objective formula is as follows:

to represent

Is estimated based on the optimization of the target,

is that

Is represented by a matrix of (a) and (b),

the optimal time-wave number phi has the following relation:

in the formula, S⁺Representing the inverse or pseudo-inverse of the matrix S.

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