CN112540381A - Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform - Google Patents
Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform Download PDFInfo
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Abstract
The invention discloses a non-vision field single-input multi-output three-dimensional reconstruction method based on non-uniform fast Fourier transform. The single-input multi-output technology is introduced for the first time in the field of non-visual field imaging, and the existing system is utilized to perform fast imaging on a non-visual field scene through non-uniform fast Fourier transform. The method comprises the following steps: adopting a laser to non-uniformly scan a reflection interface, receiving a time-photon histogram of an echo by using a detector, preprocessing received data, and converting the received time-photon data into time-amplitude data; 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 time-wave number spectrum in a time dimension; performing interpolation processing on the transformed frequency spectrum by using a single-input multiple-output frequency domain algorithm; and performing inverse fast Fourier transform on the frequency spectrum after the interpolation processing to obtain a non-view scene three-dimensional reconstruction result.
Description
Technical Field
The invention belongs to the field of laser non-visual field imaging, and particularly relates to a non-visual field three-dimensional reconstruction method based on non-uniform fast Fourier transform and single-input multi-output technology.
Background
In recent years, a non-vision field imaging technology is rapidly developed, is a novel imaging technology for performing two-dimensional or three-dimensional reconstruction on scenes outside a visual area of an observer, and has good development prospects in the aspects of complex area detection, vehicle driving assistance and medical images; the non-visual field imaging mainly utilizes the flight time data of secondary echoes of an interested detection area to reconstruct a hidden target object.
The development of non-visual field imaging is carried out through several stages, a concept of recovering a hidden object based on flight time is firstly proposed by Kirmani et al, Velten et al utilizes a stripe camera as a detector, a three-dimensional experimental reconstruction result of a non-visual field scene is firstly shown by adopting a filtering back-projection algorithm, then Buttafava et al uses a single-photon avalanche diode as a detector for non-visual field reconstruction, the early non-visual field imaging algorithms are realized by depending on a non-confocal system, and O (N) with overhigh calculation complexity exists5) And the reconstruction precision is not high.
Until 2018, O' toole et al improve the imaging system to be in a confocal mode, propose a light cone transformation algorithm to obtain reconstruction with higher precision, and reduce the algorithm complexity to O (N) as well3logN); lindell et al, using confocal systems of the same principle, introduced a frequency-wavenumber (f-k) algorithm for seismic waves, again with an algorithm complexity of O (N)3logN) and obtaining a higher accuracy reconstruction; furthermore, Liu et al have introduced the virtual wave concept in the non-viewing area for higher accuracy reconstruction.
The confocal system means that a receiving light path of a detector is the same as a transmitting light path of a laser in the imaging process, and a laser irradiation point is juxtaposed with a detector receiving point; the introduction of the confocal system simplifies an imaging light path and then a model, a receiving light path of a detector in the imaging process is the same as an emitting light path of a laser, and the imaging process is generally realized by adopting a spectroscope, but the following problems exist: the received energy is obviously attenuated; the light path design is complex; since the direct echo energy is often significantly larger than the secondary echo energy containing the reconstructed target data, the confocal design makes this phenomenon more pronounced, causing interference to the measured data.
Disclosure of Invention
The invention provides a non-vision field single-input multi-output three-dimensional reconstruction method based on non-uniform fast Fourier transform, which aims at solving the problems that the existing non-vision field imaging algorithm is realized by a non-confocal system, the calculation complexity is too high, the reconstruction precision is not high, the existing non-vision field imaging algorithm is realized by a confocal system, the optical path design is complex, the measurement data is easily interfered by secondary echo energy, and the like.
The technical scheme of the invention provides a non-view single-input multi-output three-dimensional reconstruction method based on non-uniform fast Fourier transform, which is characterized by comprising the following steps:
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 xRFor 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 isTIs 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; the number of the scanning points is M, and the value range of j is an integer from 0 to M-1;
step 2.1, for the time-amplitude data { θ ] obtained in step 1j[t]}j＝0:M-1Setting the resolution of reconstruction space, and scanning coordinate set chi and time-amplitude data thetaj[t]}j＝0:M-1Obtaining a two-dimensional non-uniform fast Fourier transform relationship in a spatial dimension, and corresponding matrixingA seed V, F, S; solving for the optimal time-wavenumber spectrum phi t, kx，ky]Minimizing the difference between the optimal time-wavenumber spectrum and the true time-wavenumber spectrum; wherein t represents time, kx、kyRepresenting 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 2.1x,ky]Performing one-dimensional fast Fourier transform in time dimension to obtain optimal frequency-wave number spectrum phi [ f, k [ ]x,ky]Where f represents frequency in the time dimension;
step 3.1, using the frequency-wavenumber relationship deduced from the dispersion relationship and adopting single-in multiple-out method to optimize the frequency-wavenumber spectrum phi [ f, kx，ky]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 compensationz，kx，ky]；
Further, in step 3.1:
in step 3.2:
in the formula, Z0Indicating the Z-axis coordinate position of the interface in reflection.
Further, step 1 specifically includes:
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
Wherein (x)T)jIs the space coordinate of the jth scanning point XOY; setting receiving point space coordinate xRAt 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 { tauj[t]}j＝0:M-1；
Wherein { }j＝0:M-1Representing a set of M elements, the element index j representing the j-th scan point (x)T)jCorresponding data, because the number of scanning points is M, the value range of j is an integer from 0 to M-1; tau isj[t]Indicating that it is at the jth scan point, i.e., (x)T)jAt time t, the number of photons received by the detector is used for corresponding data with the time-photon histogram received by the detector; 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, thetaj[t]Indicating the corresponding scanning point (x)T)jTime-amplitude data at time t.
Further, in step 2.1, a two-dimensional non-uniform fast fourier transform in the spatial dimension is obtained by:
in the formula,
representing a two-dimensional adjoint non-uniform fast Fourier transform in a spatial dimension; theta [ t, k ]x，ky]Is a time-wave number spectrum after non-uniform fast Fourier transform;
the expression after matrixing by the above formula:
Θ＝SHFHVHθ
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 algorithmx,ky]The solution objective formula is as follows:
in the formula, S+Representing the inverse or pseudo-inverse of the matrix S.
The invention has the beneficial effects that:
1. the method compares the similarity between the synthetic aperture radar model and the non-visual field model, introduces the non-visual field reconstruction into the characteristic of virtual waves, introduces a single-input multi-output algorithm into a new field, performs non-visual field imaging calculation, avoids complex and fussy back projection reconstruction by interpolation processing on a measurement data frequency domain, and greatly improves the imaging rate and precision; in the non-visual field, as the field is in a starting stage, a general means for improving the imaging rate is not provided; the accuracy improving means is single, the means of performing three-dimensional Laplace filtering on the reconstructed result is common, but the method can obtain a clear imaging result without the filtering operation.
2. The invention can be realized based on a non-confocal system, does not depend on the design of a confocal imaging system, and improves the imaging flexibility.
3. The invention utilizes the non-uniform Fourier transform and the corresponding conjugate gradient algorithm, can utilize the non-uniform data of the down sampling, and quickly and effectively recover the frequency spectrum close to the real data; the number of scanning points can be obviously reduced, and the time for collecting data by an algorithm is reduced.
4. According to the invention, by using the non-uniform Fourier transform and the corresponding conjugate gradient algorithm, the region of interest can be collected with emphasis, non-uniform data after the region of interest is collected with emphasis is obtained, data information of the region of interest is fully obtained, and the imaging flexibility is further improved. The existing non-visual field imaging algorithm has the defects that the imaging speed is too slow (such as a filtering back projection algorithm and a virtual wave algorithm) or the imaging speed is dependent on uniform data (such as a light cone transformation algorithm and a frequency wave number (f-k) algorithm of a confocal system), and the imaging speed and a data sampling mode are difficult to be compatible.
Drawings
Fig. 1 is a schematic view of a non-confocal system according to an embodiment of the present invention.
Fig. 2 is a flowchart of a non-view single-in multiple-out three-dimensional reconstruction method of non-uniform fast fourier transform according to the present invention.
FIG. 3 is a comparison graph of partial time-space data after inverse Fourier transform of the optimized spectrum and the original data according to an embodiment of the present invention.
FIG. 4 is a schematic illustration of non-view imaging results according to one embodiment of the invention.
The reference numbers in the figures are: 1-pulse laser, 2-single photon detector SPAD, 3-time correlation counting module TCSPC, 4-interface in reflection, 5-target object, 6-scanning system.
Detailed Description
The invention is further described below by means of the accompanying drawings and specific examples, which are intended to illustrate the invention and are not to be construed as limiting the invention; it should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings, and the embodiments and the features in the embodiments in the present application may be combined with each other without conflict.
The invention relates to a non-vision field imaging algorithm, which is used for the rapid high-precision imaging of a laser non-confocal system;
fig. 1 shows that a laser non-confocal system according to an embodiment of the present invention includes non-visual field imaging system elements: the system comprises a pulse laser 1, a single photon detector SPAD2, a time-dependent counting module TCSPC3, a reflective intermediate surface 4, a target object 5 and a scanning system 6; wherein the laser emits pulse signals with equal energy at high frequency, and the pulse signals are used for irradiating appointed position points on the interface 4 in reflection through the scanning system 6 and the emission optical system; the reflection interface is generally a diffuse reflector, generates a first diffuse reflection and illuminates the target object 5; the target object 5 is opposite to the scanning area, receives the photon signals of the first reflection and generates a second reflection; the photon signal of the second reflection is transmitted back to the reflection interface, and a third reflection is generated on the reflection interface; the single-photon detector SPAD2 adopts a gating mode, and only receives photon signals transmitted by third reflection, namely, so-called second echo data; by accumulation, a time-photon histogram of the echoes is generated using the time dependent counting module TCSPC 3.
Fig. 2 is a flowchart of a non-visual field three-dimensional scene reconstruction method based on non-confocal system non-uniform fast fourier transform according to an embodiment of the present invention, including the following steps:
firstly, adopting a multi-point non-uniform scanning reflection interface of a laser, receiving a time-photon histogram of an echo by using a single point of a detector, preprocessing received data, and converting the received time-photon data into time-amplitude data; as in fig. 1, "×" indicates a laser scanning point, and "●" indicates a probe receiving point.
1.1) setting an XYZ 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;
1.2) setting a multi-point non-uniform scanning coordinate set of a laser
Sampling from XOY two-dimensional space
Setting coordinates of receiving point of detector
xTIs the space coordinate of the scanning point XOY; x is the number ofRIs a receiving point XOY space coordinate, is positioned in the center of the scanning area, xR＝(0,0)；
1.3) for different scanning points, the receiver receives and accumulates to obtain a corresponding time-photon histogram set, which is recorded as:
T：＝{τj[t]}j＝0:M-1
in the formula, τj[t]Indicating that the scanning point is at (x)T)jAt time t, the number of photons received by the detector is regarded as a function of time t; for each histogram τj[t]The time t is 0 corresponding to the first arrival of the laser pulse at the scanning point (x)T)jThe time of day; wherein the length in the time dimension t is Nt；
1.4), preprocessing is performed for each histogram data as follows:
specifically, before scanning by using a laser, a non-uniform scanning mode is preset, the number of scanning points is M, and the positions of the scanning points can be random or designed; the received data is "time-photon number" data, i.e., "time-intensity" data, and therefore the received data is preprocessed to become "time-amplitude" data, which is treated as a virtual wave.
Step two, performing two-dimensional non-uniform fast Fourier transform on the data preprocessed in the step one in a space dimension and one-dimensional fast Fourier transform on a time dimension, wherein the steps comprise:
2.1), setting the reconstruction spatial resolution, adopting a multi-point non-uniform scanning coordinate set chi and the data { theta ] processed in the step 1.4j[t]}j＝0:M-1Obtaining a corresponding matrixing operator V, F, S of two-dimensional non-uniform fast Fourier transform in the space dimension, and solving the optimal time-wave number spectrum phi [ t, k ] uniformly distributed in a space dimension Cartesian coordinate system by utilizing a conjugate gradient optimization algorithmx,ky]；
The two-dimensional non-uniform fast fourier transform relationship in the spatial dimension is:
in the formula,
a two-dimensional adjoint non-uniform fast Fourier transform representing a spatial dimension; theta [ t, k ]x，ky]Representing a time-wavenumber spectrum obtained after a non-uniform fast fourier transform; wherein t represents time, kx、kyRepresenting wavenumbers in the X, Y dimensions of the two-dimensional XOY space, respectively;
wherein,
a two-dimensional adjoint non-uniform fast Fourier transform, representing a spatial dimension, is the inverse of the two-dimensional non-uniform fast Fourier transform;
the two-dimensional non-uniform fast Fourier transform is used for solving the problem of Fourier transform from uniform data to non-uniform data, and comprises the following steps: an upsampling step, selecting a basis function and smoothing non-uniform data; a fast Fourier transform step of performing fast Fourier transform on the smoothed sample data; and an interpolation step for removing the influence of the basis function on the transformation result. The above process relationship can be expressed as a combination of matrixed linear operations:
Θ＝VFSΘ
in the formula, V is an interpolation matrix; f represents a fast Fourier transform matrix; s is an upsampling matrix; theta is { thetaj[t]}j＝0:M-1A vectorized representation of (a); theta is theta [ t, k ]x，ky]A matrixed representation of; the above equation represents a data set { theta ] obtained by spatially non-uniformly scanning a point χj[t]}j＝0:M-1It can be considered as a uniform time-wavenumber spectrum Θ [ t, k ]x，ky]And obtaining the X through two-dimensional non-uniform fast Fourier transform according to the non-uniform scanning point.
The two-dimensional accompanying non-uniform fast fourier transform is an inverse process of the two-dimensional non-uniform fast fourier transform, is used for solving the problem of performing fourier transform on non-uniform data to uniform data, and the process can also be expressed as a combination of matrixed linear operations:
Θ＝SHFHVHθ
the above equation is using the data set { theta }j[t]}j＝0:M-1Solving by adopting two-dimensional accompanying non-uniform fast Fourier transform to obtain uniform time-wavenumber spectrum theta [ t, k [ ]x，ky]The process of (2); the H in the upper right hand corner of the matrix symbol represents the hermite transpose of the matrix.
However, due to the imperfection of the data acquisition from non-uniform scan points, the direct use of the results accompanying the non-uniform fast fourier transform is not ideal, especially when down-sampled reconstruction is used. Thus, the result Θ (i.e., Θ t, k) that accompanies the non-uniform fast Fourier transform is not generally used directlyx，ky]) The optimal time-wave number spectrum phi t, k with minimized difference from the real spectrum is solved by an optimization algorithm using a non-uniform Fourier transform relationshipx,ky](ii) a Optimal reconstruction of time-wavenumber spectrum phi t, kx,ky]Is expressed as phi, and the objective formula is solved by a conjugate gradient algorithm as follows:
in the formula, S+Represents the inverse or pseudo-inverse of the matrix S;
2.2), for an optimal time-wavenumber spectrum phi t, kx,ky]Performing a one-dimensional fast fourier transform in the time dimension:
in the formula,
representing a one-dimensional fast fourier transform in a time dimension t; wherein f represents frequency in the time dimension;
thirdly, performing interpolation processing on the transformed frequency spectrum by using a single-input multi-output technology:
3.1) reconstruction of three-dimensional wavenumber spectra
With measured data frequency-wavenumber spectrum phi kz,kx,ky]The mapping relationship of (1):
the mapping relation of the above formula is obtained by a single-input multiple-output frequency domain algorithm, and the reconstructed spectrum which is uniformly distributed on the wave number space and is obtained by interpolation according to the mapping relation
kzRepresents the wave number in the Z-axis direction;
3.2) adding a compensation term to perform phase compensation:
in the formula, Z0Representing the Z-axis coordinate position of the interface in reflection; Ψ represents the spectral data after adding the compensation term;
specifically, the dispersion relationship is derived from the frequency-wavenumber relationship in the non-confocal case:
reconstructing three-dimensional wavenumber spectra
Mapping relation with measured data frequency-wave number spectrum phi
Derived from the above relationship; from reconstructed three-dimensional wave number spectra
The mapping relation between the frequency-wave number spectrum phi of the measured data can be used for knowing the value of the required frequency-wave number spectrum phi
The required frequency f is not uniformly distributed on a Cartesian coordinate system, and is obtained through interpolation calculation;
fourthly, performing inverse fast Fourier transform on the frequency spectrum after interpolation processing to obtain a non-view scene three-dimensional reconstruction result:
4.1) inverse Fourier transform:
in the formula, psi three-dimensionally represents spatial domain data obtained after inverse Fourier transform;
4.2) obtaining non-view reconstruction result | ψ (z, x, y) |2
The invention is further described below with reference to specific examples.
Step one, adopting an imaging system as shown in fig. 1, adopting a laser non-uniform scanning reflection interface, adopting a mode of randomly selecting scanning points for scanning, wherein the number M of the scanning points is 2000, receiving a time-photon histogram of an echo by using a detector, preprocessing received data, and converting the received time-photon data into time-amplitude data; setting a reconstruction target as a Stanford rabbit;
step two, performing one-dimensional fast Fourier transform on time dimension and two-dimensional non-uniform fast Fourier transform on space dimension on the preprocessed data, setting the wave number domain resolution of the non-uniform fast Fourier transform to be 256 multiplied by 256, and finally reconstructing the restored data image with the resolution of 128 multiplied by 128, namely the sampling rate is 12.2%; solving the optimal time-wave number spectrum uniformly distributed on a space dimension Cartesian coordinate system by utilizing a conjugate gradient optimization algorithm; after the two-dimensional inverse Fourier transform is performed on the optimal time-wave number spectrum, the obtained partial time-space data and the original data are compared as shown in FIG. 3, so that the echo data can be obviously complemented, and the details such as the shape, the trend, the energy distribution and the like of the echo are obviously improved compared with the prior art; performing time-dimension fast Fourier transform on the time-wave number spectrum to finally obtain a frequency-wave number spectrum used in the step three;
thirdly, performing interpolation processing on the transformed frequency spectrum by using a single-input multi-output technology;
fourthly, performing inverse fast Fourier transform on the frequency spectrum subjected to interpolation processing to obtain a non-vision field scene three-dimensional reconstruction result; the reconstruction result is shown in fig. 4, and it can be seen that the reconstruction result is a stanford rabbit, which is clearly identifiable without obvious erroneous reconstruction, and the reconstruction result is fine and smooth in a region with good reflection conditions, such as a rabbit thigh close to the reflection interface; in areas with poor reflection conditions, such as rabbit ears far from the interface in reflection, the reconstructed result still has a corresponding contour.
The above examples of the present invention are given for the purpose of illustrating the present invention clearly and are not intended to limit the method of carrying out the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in 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 xRFor 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 isTIs 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 1j[t]}j＝0：M-1Setting the resolution of reconstruction space, and scanning coordinate set chi and time-amplitude data thetaj[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, kx，ky]Minimizing the difference between the optimal time-wavenumber spectrum and the true time-wavenumber spectrum; wherein t representsTime, kx、kyRepresenting 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 2.1x，ky]Performing one-dimensional fast Fourier transform in time dimension to obtain optimal frequency-wave number spectrum phi [ f, k [ ]x，ky]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，ky]Interpolation processing is carried out, and spectrum psi [ k ] is obtained after compensationz，kx，ky](ii) a Wherein k iszRepresents 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, kx，ky]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 compensationz，kx，ky]；
Step 4, aiming at the frequency spectrum psi [ k ] after phase compensationz，kx，ky]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 xRAt 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 { tauj[t]}j＝0：M-1；
Wherein, tauj[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 isTIs 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, thetaj[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，ky]Is a time-wave number spectrum after non-uniform fast Fourier transform;
the expression after matrixing by the above formula:
Θ＝SHFHVHθ
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 algorithmx，ky]The solution objective formula is as follows:
in the formula, S+Representing the inverse or pseudo-inverse of the matrix S.
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