CN112540381B - 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 PDF

Info

Publication number
CN112540381B
CN112540381B CN202011288854.6A CN202011288854A CN112540381B CN 112540381 B CN112540381 B CN 112540381B CN 202011288854 A CN202011288854 A CN 202011288854A CN 112540381 B CN112540381 B CN 112540381B
Authority
CN
China
Prior art keywords
time
fourier transform
fast fourier
spectrum
uniform
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011288854.6A
Other languages
Chinese (zh)
Other versions
CN112540381A (en
Inventor
苏秀琴
徐伟豪
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
XiAn Institute of Optics and Precision Mechanics of CAS
Original Assignee
XiAn Institute of Optics and Precision Mechanics of CAS
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by XiAn Institute of Optics and Precision Mechanics of CAS filed Critical XiAn Institute of Optics and Precision Mechanics of CAS
Priority to CN202011288854.6A priority Critical patent/CN112540381B/en
Publication of CN112540381A publication Critical patent/CN112540381A/en
Application granted granted Critical
Publication of CN112540381B publication Critical patent/CN112540381B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/88—Lidar systems specially adapted for specific applications
    • G01S17/89—Lidar systems specially adapted for specific applications for mapping or imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/4802—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/491—Details of non-pulse systems
    • G01S7/4912—Receivers

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Electromagnetism (AREA)
  • Image Analysis (AREA)

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; for the preprocessed data, an optimization algorithm is utilized, an optimal time-wave number spectrum is solved through a two-dimensional non-uniform fast Fourier transform relation of a space dimension, and then one-dimensional fast Fourier transform on the time dimension is carried out on the time-wave number spectrum; 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 subjected to the interpolation processing to obtain a non-view scene three-dimensional reconstruction result.

Description

Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform
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 from Kirmani et al, velten et al utilizes a stripe camera as a detector and adopts a filtering back projection algorithm to firstly display a three-dimensional experimental reconstruction result of a non-visual field sceneLater to Buttafava et al, the single photon avalanche diode is used as a detector for non-vision field reconstruction, and these early stage non-vision field imaging algorithms are realized by a non-confocal system, and O (N) with overhigh calculation complexity exists 5 ) 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 well 3 logN); 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) 3 logN) and obtaining higher precision 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 simplifies 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-visual field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform, which is characterized by comprising the following steps:
step 1, preprocessing data;
adopting a laser multipoint non-uniform scanning reflection interface, wherein the number of scanning points is M, and obtaining a multipoint non-uniform scanning coordinate set
Figure BDA0002783261900000021
And using a single point of the detector to receive the time-photon histogram data of the echo, setting x R For receiving point XOY space coordinate, preprocessing time-photon histogram data, and converting the time-photon histogram data into time-amplitude data { theta } j [t]} j＝0:M-1 (ii) a Wherein x is T Is the space coordinate of the scanning point XOY { } j＝0:M-1 Representing a set of M elements, the element index j representing the jth scan point (x) T ) j Corresponding 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, 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 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-1 Setting the resolution of reconstruction space, and scanning coordinate set chi and time-amplitude data theta j [t]} j＝0:M-1 Obtaining a two-dimensional non-uniform fast Fourier transform relation on a space dimension and corresponding matrixing operators V, F and S; solving the optimal time-wave number spectrum phi t, k x ，k y ]Minimizing the difference between the optimal time-wavenumber spectrum and the true time-wavenumber spectrum; wherein t represents time, k x 、k y Representing wave numbers of the two-dimensional XOY space in X and Y dimensions 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 (ii) of3. Using single-in multi-out frequency domain algorithm to process 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 z Represents the wave number in the Z-axis direction;
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, k x ，k y ]Performing interpolation calculation to obtain spectrum after interpolation calculation
Figure BDA0002783261900000033
Step 3.2, the frequency spectrum after interpolation calculation
Figure BDA0002783261900000034
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.
Further, in step 3.1:
Figure BDA0002783261900000031
in step 3.2:
Figure BDA0002783261900000032
in the formula, Z 0 Indicating 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 multiple lasersPoint non-uniform scanning coordinate to obtain multi-point non-uniform scanning coordinate set
Figure BDA0002783261900000041
Wherein (x) T ) j Is the space coordinate of the jth scanning point XOY; setting receiving point space coordinate x R At the center of the scanning area;
step 1.3, for different scanning points, the detector cumulatively receives to obtain a corresponding time-photon histogram data set { tau } j [t]} j＝0:M-1 ；
Wherein { } j＝0:M-1 Representing a set of M elements, the element index j representing the jth scan point (x) T ) j Corresponding data, because the number of scanning points is M, the value range of j is an integer from 0 to M-1; tau. j [t]Indicating that it is at the jth scan point, i.e., (x) T ) j At the time of t, the number of photons received by the detector is used for corresponding data of 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;
Figure BDA0002783261900000042
in the formula, theta j [t]Indicating the corresponding scanning point (x) T ) j Time-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:
Figure BDA0002783261900000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002783261900000044
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 above formula is matrixed expression:
Θ＝S H F H V H θ
v, F and S are non-uniform fast Fourier transform corresponding matrixing operators, and V is an interpolation matrix; f denotes 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:
Figure BDA0002783261900000051
Figure BDA0002783261900000052
to represent
Figure BDA0002783261900000053
Is estimated based on the optimization of the target,
Figure BDA0002783261900000054
is that
Figure BDA0002783261900000055
Is represented by a matrix of (a) and (b),
Figure BDA0002783261900000056
the following relationship to the optimal time-wavenumber Φ:
Figure BDA0002783261900000057
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 low (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 diagram 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 device comprises a pulse laser 1, a single photon detector SPAD2, a time correlation counting module TCSPC3, a reflection medium 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 reflecting interface 4 through the scanning system 6 and the emission optical system; the reflective interface is generally a diffuse reflector, which generates a first diffuse reflection to illuminate 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 middle reflection interface, and a third reflection is generated on the middle reflection interface; the single-photon detector SPAD2 adopts a gating mode, and only receives photon signals transmitted by the third reflection, namely the so-called second echo data; by accumulation, a time-photon histogram of the echoes is generated, using a 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:
step one, adopting a laser multipoint non-uniform scanning reflection interface, receiving a time-photon histogram of an echo by using a detector single point, preprocessing received data, and converting the received time-photon data into time-amplitude data; as in fig. 1, "×" indicates a laser scanning point, "\9679;" indicates a detector receiving point.
1.1 XYZ world coordinate system is set; the XOY plane is superposed with the reflective intermediate surface, 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 Multiple-point non-uniform scanning coordinate set for setting laser
Figure BDA0002783261900000071
Figure BDA0002783261900000072
Sampling from an XOY two-dimensional space
Figure BDA0002783261900000073
Setting coordinates of receiving points of detector
Figure BDA0002783261900000074
x T Is the XOY space coordinate of the scanning point; x is a radical of a fluorine atom R Is a receiving point XOY space coordinate, is positioned in the center of the scanning area, x R ＝(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：＝{τ j [t]} j＝0:M-1
in the formula, τ j [t]Indicating that the scanning point is at (x) T ) j At time t, the number of photons received by the detector is regarded as a function of time t; for each histogram τ j [t]The time t =0 corresponds to the first arrival of a laser pulse at the scanning spot (x) T ) j Time of day (c); wherein the length in the time dimension t is N t ；
1.4 For each histogram data), pre-processing is performed as follows:
Figure BDA0002783261900000081
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 ) and setting the resolution of the reconstruction space, adopting a multi-point non-uniform scanning coordinate set chi and the data processed in the step 1.4 { theta } j [t]} j＝0:M-1 Obtaining two-dimensional non-uniform fast Fourier transform corresponding matrixing operators V, F and S on the space dimension, and solving the optimal time-wave number spectrum phi [ t, k ] uniformly distributed on the space dimension Cartesian coordinate system by utilizing a conjugate gradient optimization algorithm x ,k y ]；
The two-dimensional non-uniform fast fourier transform in spatial dimension is as follows:
Figure BDA0002783261900000082
in the formula (I), the compound is shown in the specification,
Figure BDA0002783261900000083
a two-dimensional adjoint non-uniform fast Fourier transform representing a spatial dimension; theta [ t, k ] x ，k y ]Representing a time-wave number spectrum obtained after non-uniform fast Fourier transform; wherein t represents time, k x 、k y Representing wave numbers of the two-dimensional XOY space in X and Y dimensions respectively;
wherein the content of the first and second substances,
Figure BDA0002783261900000091
two-dimensional concomitant inhomogeneity representing a spatial dimensionUniform fast fourier transform, which is the inverse of 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 denotes a fast fourier transform matrix; s is an upsampling matrix; theta is { theta j [t]} j＝0:M-1 A vectorized representation of (a); theta is theta [ t, k ] x ，k y ]A matrixed representation of; the above equation represents a data set { θ } obtained by spatially non-uniform scanning of the point χ j [t]} j＝0:M-1 It can be considered as a uniform time-wavenumber spectrum Θ [ t, k ] x ，k y ]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＝S H F H V H θ
the above equation is using the data set θ j [t]} j＝0:M-1 Solving by adopting two-dimensional accompanying non-uniform fast Fourier transform to obtain uniform time-wavenumber spectrum theta [ t, k [ ] x ，k y ]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 directly x ，k y ]) 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 relationship x ,k y ](ii) a Optimal reconstruction of time-wavenumber spectrum phi t, k x ,k y ]Is expressed as phi, and the objective formula is solved by a conjugate gradient algorithm as follows:
Figure BDA0002783261900000101
Figure BDA0002783261900000102
to represent
Figure BDA0002783261900000103
Is estimated based on the optimization of the target,
Figure BDA0002783261900000104
is that
Figure BDA0002783261900000105
Is an intermediate variable of the calculation process,
Figure BDA0002783261900000106
the optimal time-wave number phi for solving the estimation has the following relation:
Figure BDA0002783261900000107
in the formula, S + Represents the inverse or pseudo-inverse of the matrix S;
2.2 For optimal time-wavenumber spectrum phi t, k) x ,k y ]Performing a one-dimensional fast fourier transform in the time dimension:
Figure BDA0002783261900000108
in the formula (I), the compound is shown in the specification,
Figure BDA0002783261900000109
representing a one-dimensional fast fourier transform in a time dimension t; wherein f represents frequency in the time dimension;
thirdly, interpolation processing is carried out on the transformed frequency spectrum by utilizing a single-input multi-output technology:
3.1 ) reconstructing a three-dimensional wave number spectrum
Figure BDA00027832619000001010
And the frequency-wavenumber spectrum phi k of the measured data z ,k x ,k y ]The mapping relation of (c):
Figure BDA00027832619000001011
the mapping relation of the above formula is obtained by a single-input multiple-output frequency domain algorithm, and a reconstructed spectrum which is uniformly distributed on a wave number space and is obtained by interpolation according to the mapping relation
Figure BDA00027832619000001012
k z Represents the wave number in the Z-axis direction;
3.2 Add a compensation term) to perform phase compensation:
Figure BDA00027832619000001013
in the formula, Z 0 Representing 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:
Figure BDA0002783261900000111
Figure BDA0002783261900000112
reconstructing three-dimensional wavenumber spectra
Figure BDA0002783261900000113
Mapping relation with measured data frequency-wave number spectrum phi
Figure BDA0002783261900000114
Derived from the above relationship; from reconstructed three-dimensional wave number spectra
Figure BDA0002783261900000115
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
Figure BDA0002783261900000116
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):
Figure BDA0002783261900000117
in the formula, psi three-dimensionally represents spatial domain data obtained after inverse Fourier transform;
4.2 Obtain non-viewing field reconstruction result | ψ (z, x, y) & gt 2
The invention is further described with reference to specific examples.
Step one, adopting an imaging system shown in figure 1, adopting a laser non-uniform scanning reflection interface, adopting a mode of randomly selecting scanning points for scanning, wherein the number of the scanning points is M =2000, and a detector is used for receiving a time-photon histogram of an echo, 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 resolution of a restored data image to be 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;
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. It need not be, and cannot be 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;
multipoint non-uniform scanning reflection by laserThe number of scanning points is M to obtain a multi-point non-uniform scanning coordinate set
Figure FDA0002783261890000011
And using a single point of the detector to receive the time-photon histogram data of the echo, setting x R For 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 T Is the space coordinate of the scanning point XOY { } j＝0：M-1 Representing a set of M elements, the element index j representing the j-th scan point (x) T ) j Corresponding 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-1 Setting the resolution of reconstruction space, and scanning coordinate set chi and time-amplitude data theta j [t]} j＝0：M-1 Obtaining a two-dimensional non-uniform fast Fourier transform relation in a space dimension and corresponding matrixing operators V, F and 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 represents time, k x 、k y Representing wave numbers of the two-dimensional XOY space in X and Y dimensions 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 z Represents the wave number in the Z-axis direction;
step 3.1, using the frequency-wavenumber relation deduced from the dispersion relation to apply a single-in multiple-out method to the optimal frequency-wavenumber spectrum phi [ f, k ] x ，k y ]Performing interpolation calculation to obtain spectrum after interpolation calculation
Figure FDA0002783261890000021
Step 3.2, spectrum after interpolation calculation
Figure FDA0002783261890000022
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:
Figure FDA0002783261890000023
in step 3.2:
Figure FDA0002783261890000024
in the formula, Z 0 Indicating 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
Figure FDA0002783261890000025
Setting receiving point space coordinate x R At the center of the scanning area;
step 1.3, for different scanning points, the detector cumulatively 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 ) j At the time t, the number of photons received by the detector is counted; wherein x is T Is the XOY space coordinate of the scanning point; subscript T represents a scanning point, corresponding to subscript R of the reception point;
step 1.4, preprocessing a time-photon histogram data set;
Figure FDA0002783261890000031
in the formula, theta j [t]Indicating the corresponding scanning point (x) T ) j Time-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:
Figure FDA0002783261890000032
in the formula (I), the compound is shown in the specification,
Figure FDA0002783261890000033
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 above formula is matrixed expression:
Θ＝S H F H V H θ
v, F and S are non-uniform fast Fourier transform corresponding matrixing operators, and 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:
Figure FDA0002783261890000034
Figure FDA0002783261890000035
represent
Figure FDA0002783261890000036
Is estimated on the basis of the optimization of (c),
Figure FDA0002783261890000037
is that
Figure FDA0002783261890000038
Is represented by a matrix of (a) and (b),
Figure FDA0002783261890000039
the optimal time-wave number phi has the following relation:
Figure FDA00027832618900000310
in the formula, S + Representing the inverse or pseudo-inverse of the matrix S.
CN202011288854.6A 2020-11-17 2020-11-17 Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform Active CN112540381B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011288854.6A CN112540381B (en) 2020-11-17 2020-11-17 Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011288854.6A CN112540381B (en) 2020-11-17 2020-11-17 Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform

Publications (2)

Publication Number Publication Date
CN112540381A CN112540381A (en) 2021-03-23
CN112540381B true CN112540381B (en) 2023-02-10

Family

ID=75014257

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011288854.6A Active CN112540381B (en) 2020-11-17 2020-11-17 Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform

Country Status (1)

Country Link
CN (1) CN112540381B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113837969B (en) * 2021-09-28 2024-05-10 宁波未感半导体科技有限公司 Non-line-of-sight image reconstruction method, device, system and computer readable storage medium
CN113820726B (en) * 2021-09-30 2023-06-13 中国科学院光电技术研究所 Noise suppression method based on multidimensional filtering in non-visual field target detection
CN115079203B (en) * 2022-05-19 2024-04-12 中国科学院西安光学精密机械研究所 Non-vision imaging system and imaging method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106054183A (en) * 2016-04-29 2016-10-26 深圳市太赫兹科技创新研究院有限公司 Three-dimensional image reconstruction method and device based on synthetic aperture radar imaging
CN106338732A (en) * 2016-08-23 2017-01-18 华讯方舟科技有限公司 Millimeter wave 3D holographic imaging method and millimeter wave 3D holographic imaging system
CN108957450A (en) * 2018-07-10 2018-12-07 西安恒帆电子科技有限公司 A kind of millimetre-wave radar GPU real time three-dimensional imaging method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20190346545A1 (en) * 2016-12-13 2019-11-14 Duke University Single-frequency dynamic metasurface microwave imaging systems and methods of use

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106054183A (en) * 2016-04-29 2016-10-26 深圳市太赫兹科技创新研究院有限公司 Three-dimensional image reconstruction method and device based on synthetic aperture radar imaging
CN106338732A (en) * 2016-08-23 2017-01-18 华讯方舟科技有限公司 Millimeter wave 3D holographic imaging method and millimeter wave 3D holographic imaging system
CN108957450A (en) * 2018-07-10 2018-12-07 西安恒帆电子科技有限公司 A kind of millimetre-wave radar GPU real time three-dimensional imaging method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
基于近似波数域算法的干涉合成孔径显微技术;李乔等;《中国激光》;20101110(第11期);全文 *
基于非均匀快速傅里叶变换的最小二乘反演地震数据重建;孟小红等;《地球物理学报》;20080115(第01期);全文 *

Also Published As

Publication number Publication date
CN112540381A (en) 2021-03-23

Similar Documents

Publication Publication Date Title
CN112540381B (en) Non-vision field single-in multi-out three-dimensional reconstruction method based on non-uniform fast Fourier transform
EP2915180B1 (en) Fourier ptychographic imaging systems, devices, and methods
Fienup Space object imaging through the turbulent atmosphere
Blahut Theory of remote image formation
Solimene et al. Three-dimensional through-wall imaging under ambiguous wall parameters
CN103592030B (en) The full polarization hyperspectral detection device of fast illuminated integration view field imaging
US20220206434A1 (en) System and method for deep learning-based color holographic microscopy
CN112904368A (en) Non-visual field three-dimensional reconstruction method and system based on analytic signal and compensation reference function
CN109613556B (en) Photon counting laser three-dimensional detection imaging method based on sparse representation
Vine et al. Ptychographic Fresnel coherent diffractive imaging
CN103592029B (en) Snapshot calculation tomography imaging full-polarization hyperspectral detection device
WO2015063779A1 (en) System and method for phase retrieval in lensless imaging
CN110554384A (en) imaging method based on microwave signal
CN114965470A (en) Light intensity transmission diffraction chromatography microimaging method based on non-interference synthetic aperture
CN101660945A (en) Quick image reconstruction method
Vasileiou et al. Efficient CNN-based super resolution algorithms for mmWave mobile radar imaging
CN112634380A (en) Multi-target color scattering imaging method for single-frame hyper-optical memory effect
Rodet et al. Data inversion for over-resolved spectral imaging in astronomy
Martín-del-Campo-Becerra et al. Resolution enhancement of spatial parametric methods via regularization
Laub et al. Three-dimensional object representation in imaging systems
Stott et al. Three-dimensional imaging with a quadrature tomographic microscope
WO2019140434A2 (en) Overlapping pattern differentiation at low signal-to-noise ratio
CN110850432A (en) Method for resolving reflectivity distribution of laser reflection tomography target
CN113702939B (en) Near-field local irradiation target scattering near-far field conversion method
Borden Regularization of noisy ISAR images containing extended features

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant