CN112904368B - Non-visual field three-dimensional reconstruction method and system based on analytic signal and compensation reference function - Google Patents
Non-visual field three-dimensional reconstruction method and system based on analytic signal and compensation reference function Download PDFInfo
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Abstract
The application discloses a non-visual field three-dimensional reconstruction method and system based on an analytic signal and a compensation reference function. The method solves the problems of the existing non-vision imaging algorithm, such as high computational complexity, low reconstruction accuracy, complex optical path design, easy interference of secondary echo energy on measured data, and the like, and comprises the following steps: firstly, converting received time-photon data into time-amplitude data, and performing Hilbert transformation to obtain an analytic signal; secondly, carrying out three-dimensional Fourier transform on the analysis signal, and multiplying the wave number spectrum after transformation by a compensation-reference function; thirdly, after the wave number spectrum is subjected to transverse inverse Fourier transform, multiplying by a transverse phase operator, and then, after the transverse Fourier transform, carrying out longitudinal Stokes interpolation; thirdly, compensating the wave number spectrum after the transverse inverse Fourier transform by using a transverse phase compensation function; and finally, performing longitudinal inverse Fourier transform to obtain the target three-dimensional reconstruction.
Description
Technical Field
The application belongs to the field of laser non-visual field imaging, and particularly relates to a non-visual field three-dimensional reconstruction method based on an analytic signal and a compensation reference function.
Background
In recent years, a non-visual field imaging technology is rapidly developed, and the non-visual field imaging technology is a novel imaging technology for reconstructing a scene outside a visual field of an observer in two dimensions or three dimensions, and has good development prospects in the aspects of complex area detection, vehicle driving assistance and medical imaging; the non-field of view imaging mainly utilizes the flight time data of the secondary echo of the detection region of interest to reconstruct the hidden target object.
The development of non-field of view imaging has gone through several stages, the concept of recovering hidden objects based on time of flight was first proposed from Kirmani et al, velten et al utilized a striped camera as detector, a filtered back projection algorithm was employed to first demonstrate the three-dimensional experimental reconstruction of non-field of view scenes, and then to Buttafava et al utilized single photon avalanche diodes as detectors for non-field of view reconstruction, these earlier stagesThe non-vision imaging algorithm depends on the implementation of a non-confocal system, and has the problem of excessively high computational complexity O (N 5 ) The reconstruction accuracy is not high.
Until 2018, O' tool et al improved the imaging system to be confocal mode, put forward the light cone transformation algorithm to obtain higher accuracy reconstruction, the algorithm complexity also reduced to O (N) 3 log n); lindell et al uses the same principle confocal system, introduces the frequency wave number (f-k) algorithm of seismic waves, and the same algorithm complexity is O (N 3 log n) and a higher accuracy reconstruction is obtained; in addition, liu et al introduce virtual wave concepts in the non-field of view for higher accuracy reconstruction.
The confocal system refers to 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 the receiving point of the detector; the introduction of the confocal system simplifies an imaging model, the receiving light path of the detector is the same as the transmitting light path of the laser in the imaging process, and the confocal system is generally realized by adopting a spectroscope, but has the following problems: the received energy is significantly attenuated; the light path design is complex, and the direct echo energy is often obviously larger than the secondary echo energy containing the reconstructed target data, so that the confocal design can make the phenomenon more obvious, and the measured data can be interfered.
Disclosure of Invention
Aiming at the problems of high computational complexity, low reconstruction precision and the like existing in the conventional non-vision imaging algorithm which are realized by a non-confocal system, the problems of complex optical path design, easiness in interference of secondary echo energy on measured data and the like existing in the confocal system, the application provides a non-vision three-dimensional reconstruction method and a system based on an analytic signal and a compensation reference function.
The technical scheme of the application is to provide a non-visual field three-dimensional reconstruction method based on an analytic signal and a compensation reference function, which is characterized by comprising the following steps:
step 1, data preprocessing;
receive time-photon data τx R ,y R ；x T ,y T ,t]Conversion to time-amplitude data ψ [ x ] R ,t R ；x T ,y T ,t]For psi [ x ] R ,y R ；x T ,y T ,t]Hilbert transform is performed to obtain psi H [x R ,y R ；x T ,y T ,t]To psi H [x R ,y R ；x T ,y T ,t]Resolving to obtain resolved signal psi A [x R ,y R ；x T ,y T ,t]The method comprises the steps of carrying out a first treatment on the surface of the Where t represents the time of arrival of the time-recorded photon, (x) R ,y R ) For receiving the point XOY spatial coordinates, (x T ,y T ) The scanning point XOY space coordinates; the XOY plane coincides with the reflective intermediate plane;
step 2, analyzing the signal psi A [x R ,y R ；x T ,y T ,t]Performing three-dimensional Fourier transform, and compensating the wave number spectrum after transformation by using a compensation-reference function;
step 2.1, analyzing the signal ψ A [x R ,y R ；x T ,y T ,t]Performing three-dimensional Fourier transform to obtain a wave number spectrum psi after transformation 1 [x R ,y R ；k xT ,k yT ,k]；k xT ,k yT K represents x T ,y T T is the wave number domain, k corresponding to the three-dimensional Fourier transform xT Representing the scan abscissa x T Wave number domain, k, corresponding to three-dimensional Fourier transform yT Representing the scanning ordinate y T A wave number domain corresponding to the three-dimensional Fourier transform, wherein k represents a wave number domain corresponding to the time t after the three-dimensional Fourier transform;
step 2.2, setting a reconstruction region reference point (x 0 ,y 0 ,z 0 ) And calculate the compensation-reference function phi based thereon CRFM [x R ,y R ；k xT ,k yT ,k]；
Step 2.3 wave number Spectrum ψ 1 [x R ,y R ；k xT ,k yT ,k]Multiplying the compensation-reference function phi CRFM [x R ,yR；k xT ,k yT ,k]Obtaining wave number spectrum ψ 2 [x R ,y R ；k xT ,k yT ,k]；
Step 3, for wave number spectrum ψ 2 [x R ,y R ；k xT ,k yT ,k]Multiplying a transverse phase operator after transverse inverse Fourier transform, and then carrying out Stokes interpolation in a longitudinal dimension after transverse Fourier transform;
step 3.1, vs. wave number Spectrum ψ 2 [x R ,y R ；k xT ,k yT ,k]Performing transverse inverse Fourier transform to obtain psi 2 [x R ,y R ；x T ,y T ,k]；
Step 3.2, calculating the transverse phase operator phi shift [x R ,y R ；x T ,y T ,k]；
Step 3.3, ψ 2 [x R ,y R ；x T ,y T ,k]Multiplying by transverse phase operator Φ shift [x R ,y R ；x T ,y T ,k]And performing transverse fast Fourier transform to obtain ψ 3 [x R ,y R ；k x ,k y ,k]The method comprises the steps of carrying out a first treatment on the surface of the Wherein k is x Representing the wavenumber domain, k, corresponding to the Fourier transform of the dimension corresponding to the space abscissa x with the reference point as the center y Representing a wave number domain corresponding to the space ordinate y taking the reference point as the center after the dimension Fourier transform, and k represents a wave number domain corresponding to the space ordinate y after the time t dimension Fourier transform;
step 3.4 for wave number spectrum ψ 3 [x R ,y R ；k x ,k y ,k]Performing Stokes interpolation in the longitudinal dimension to obtain a wavenumber spectrum ψ 4 [x R ,y R ；k x ,k y ,k z ]；k z Representing a wave number domain corresponding to the space depth coordinate z taking the reference point as the center after the dimension Fourier transform;
step 4, utilizing a transverse phase compensation function to correct the psi 4 [x R ,y R ；k x ,k y ,k z ]Compensating the wave number spectrum after the transverse inverse Fourier transform;
step 4.1, calculating a transverse phase compensation function phi E1 [x,y,k z ]；
Step 4.2, pair ψ 4 [x R ,y R ；k x ,k y ,k z ]Performing fast inverse Fourier transform on the transverse dimension of (2) to obtain phi 4 [x R ,y R ；x,y,k z ]；
Step 4.3, ψ 4 [x R ,y R ；x,y,k z ]Multiplying by a transverse phase compensation function phi E1 [x,y,k z ]To compensate the phase change caused by multiplying the reference function to obtain a compensated wave number spectrum psi 5 [x R ,y R ；x,y,k z ]；
Step 5, performing longitudinal inverse Fourier transform to obtain a target three-dimensional reconstruction;
step 5.1 for wavenumber spectrum ψ 5 [x R ,y R ；x,y,k z ]Performing longitudinal inverse Fourier transform to obtain a reconstruction result psi of the three-dimensional space domain 6 [x R ,y R ；x,y,z]；
Step 5.2, processing ψ according to the following 6 [x R ,y R ；x,y,z]Obtaining a final reconstruction result ρx R ,y R ；x,y,z]；
ρ[x R ,y R ；x,y,z]＝|ψ 6 [x R ,y R ；x,y,z]| 2 。
Further, in step 2.2:
in the method, in the process of the application,for parameters related to reference point settings, the regional reference point (x 0 ,y 0 ,z 0 ) Selecting the center of a reconstruction area, wherein exp {. Cndot. } represents an exponential function taking a natural number e as a base number; compensation-reference function left-hand multiplier: />As the amplitude term of the reference function, which functions to provide "compensation", compensates for the attenuation of energy during optical transmission, the compensation-reference function is the right-hand multiplier:for the compensation-reference function phase term, which acts to provide a "reference" for coarse focusing of the range around the reference point; i represents an imaginary number.
Further, in step 1:
ψ A [x R ,y R ；x T ,y T ,t]＝ψ[x R ,y R ；x T ,y T ,t]+iψ H [x R ,y R ；x T ,y T ,t]
in the method, in the process of the application,representing the hilbert transform with respect to time t, i representing the imaginary number.
Further, in step 3.2):
Φ Shift [x R ,y R ；x T ,y T ,k]＝exp{-i2πk(a 1 x T +b 1 y T )}
wherein a is 1 ,b 1 Is a function R R (x,y,z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ,y 0 ,z 0 ) A first order coefficient term for taylor expansion.
Further, in step 3.4)
Wherein a is 1 ,b 1 ,c 1 Is a function R R (x,y,z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ,y 0 ,z 0 ) A first order coefficient term for taylor expansion.
The application also provides a non-visual field three-dimensional reconstruction system based on the analytic signal and the compensation reference function, which comprises a processor and a memory, wherein the memory stores a computer program, and is characterized in that: when the computer program is executed by a processor, the non-visual field three-dimensional reconstruction method based on the analytic signal and the compensation reference function is realized.
The present application also provides a computer-readable storage medium having stored thereon a computer program, characterized in that: when the computer program is executed by a processor, the non-visual field three-dimensional reconstruction method based on the analytic signal and the compensation reference function is realized.
The beneficial effects of the application are as follows:
1. according to the application, through comparing the similarity between the synthetic aperture radar model and the non-visual field model, an Omega-K Algorithm (Omega-K Algorithm) Algorithm in the radar field is introduced into the new field to perform non-visual field imaging calculation, and through interpolation processing on the measured data frequency domain, complex and tedious back projection reconstruction is avoided, so that the imaging speed and the imaging precision are greatly improved; the non-vision field is in a starting stage, so that a universal means for improving the imaging rate is not available; the method for improving the precision is single, and the method for performing three-dimensional Laplacian filtering on the reconstructed result is common, but the method does not need to perform additional filtering treatment on the reconstructed result;
2. the application combines the non-visual field process characteristics, deduces and improves the reference function of the original omega KA algorithm into the compensation-reference function, compensates the attenuation of partial energy in the light transmission process, and the improvement ensures that the modeling is more targeted and the reconstruction result is clearer;
3. the application improves and supplements the signal by solving the analytic signal of the data; the analytic signal is introduced into a complex domain, so that the signal is ' upscaled ', and the signal is smoother ', which is the perfection of the signal; the spectrum of the Hilbert transform of the data can be understood as the spectrum of the derivative of the data after adding the low-pass filter in the frequency domain, so that the signal contains more information, which is a supplement to the signal;
4. the application can be realized based on a non-confocal system, does not depend on the confocal imaging system design, does not require the position of a receiving point, and improves the imaging flexibility.
Drawings
Fig. 1 is a schematic diagram of a non-confocal system according to an embodiment of the application.
Fig. 2 is a flowchart of a non-view three-dimensional reconstruction method based on an analytic signal and a compensation reference function.
Fig. 3 is a simulation scenario provided in an embodiment of the present application.
Fig. 4 is a simulation reconstruction result provided by the embodiment of the present application.
The reference numerals in the drawings 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 application is further described below by means of the attached drawings and specific examples, which are intended to illustrate the application, but not to be construed as limiting the application; for convenience of description, only the portions related to the present application are shown in the drawings, and the embodiments of the present application and the features of the embodiments may be combined with each other without conflict.
The non-visual field imaging algorithm is used for rapid high-precision imaging of a laser non-confocal system; fig. 1 shows a non-field of view imaging system comprising a laser non-confocal system, comprising a pulsed 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 pulse laser 1 emits pulse signals with equal energy at high frequency, and irradiates a designated position point on the interface 4 in reflection through the scanning system 6; the interface 4 is typically a diffuse reflector, which produces a first diffuse reflection to illuminate the target object 5; the target object 5 is opposite to the scanning area, receives the photon signal of the first reflection and generates the second reflection; the photon signal reflected for the second time is transmitted back to the intermediate reflection surface 4, and a third reflection is generated on the intermediate reflection surface 4; the SPAD2 of the single photon detector adopts a gating mode and only receives photon signals transmitted by tertiary reflection, namely 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-view three-dimensional reconstruction method based on an analytic signal and a compensation reference function, which includes the following steps:
step one, adopting a laser multipoint scanning reflection medium interface, using a gating detector to receive a time-photon histogram of echo at a single point, converting received time-photon data into time-amplitude data, and performing Hilbert transformation to obtain an analysis signal; as in fig. 1, "×" indicates a laser scanning point, "+% indicates a detector receiving point;
1.1 Setting an XYZ world coordinate system; wherein the XOY plane coincides with the reflective intermediate plane, the Z axis is perpendicular to the XOY plane, and the positive direction of the Z axis points to the non-visual field scene;
1.2 Setting (x) R ,y R ) Is connected withThe coordinates of the endpoint XOY space, (x) T ,y T ) The scanning point XOY space coordinates;
1.3 For a scan point (x) T ,y T ) At point (x R ,y R ) The receiver receives the accumulation and uses gating to intercept the non-view portion to obtain a corresponding time-photon histogram, denoted as τx R ,y R ；x T ,y T ,t]Wherein t represents time of arrival of time-recorded photons, and uniformly scanning the non-view scanning region to obtain different scanning points (x T ,y T ) Time-photon histograms of (a);
1.4 For each histogram data, preprocessing is performed as follows:
1.5 Hilbert transform is performed on the pre-processed signal to obtain ψ H And obtain its analytic signal psi A The following are provided:
ψ A [x R ,y R ；x T ,y T ,t]＝ψ[x R ,y R ；x T ,y T ,t]+iψ H [x R ,y R ；x T ,y T ,t]
in the method, in the process of the application,representing the Hilbert transform over time t, i representing the imaginary number, the pre-processed signal being ψ x R ,y R ；x T ,y T ,t]The Hilbert transform signal of the pre-processed signal is ψ H [x R ,y R ；x T ,y T ,t]Resolving the signal to be psi A [x R ,yR；x T ,y T ,t]；
Step two, performing three-dimensional Fourier transform on the analytic signal, and multiplying the transformed frequency spectrum by a compensation-reference function;
2.1 For resolving signal psi A [x R ,y R ；x T ,y T ,t]Performing three-dimensional Fourier transform to obtain a wave number spectrum psi after transformation 1 [x R ,y R ；k xT ,k yT ,k]The following are provided:
in the method, in the process of the application,representation about x T ,y T Fast fourier transform of t, k xT ,k yT K represents x T ,y T T is a wave number domain corresponding to Fourier transform;
2.2 Setting a reconstruction region reference point (x) 0 ,y 0 ,z 0 ) And calculate the compensation-reference function phi based thereon CRFM [x R ,y R ；k xT ,k yT ,k]The following are provided:
in the method, in the process of the application,for parameters related to reference point settings, the regional reference point (x 0 ,y 0 ,z 0 ) Selecting the center of a reconstruction area, wherein exp {. Cndot. } represents an exponential function taking a natural number e as a base number; compensation-reference function left-hand multiplier: />As the amplitude term of the reference function, which functions to provide "compensation", compensates for the attenuation of energy during optical transmission, the compensation-reference function is the right-hand multiplier:for the compensation-reference function phase term, which acts to provide a "reference" for coarse focusing of the range around the reference point;
2.3 Wavenumber spectrum ψ 1 [x R ,y R ；k xT ,k yT ,k]Multiplying the compensation-reference function phi CRFM [x T ,y R ；k xT ,k yT ,k]Obtaining wave number spectrum ψ 2 [x R ,y R ；k xT ,k yT ,k]The following are provided:
Ψ 2 [x R ,y R ；k xT ,k yT ,k]＝Ψ 1 [x R ,y R ；k xT ,k yT ,k]·Φ CRFM [x R ,y R ；k xT ,k yT ,k]
step three, multiplying the wave number spectrum by a transverse phase operator after transverse inverse Fourier transform, and then carrying out Stokes interpolation in the longitudinal dimension after transverse dimension fast Fourier transform;
3.1 Wavenumber spectrum ψ 2 [x R ,y R ；k xT ,k yT ,k]The transverse inverse fourier transform is as follows:
in the method, in the process of the application,representation for wave number k xT ,k yT Is an inverse fast fourier transform of (a);
3.2 Calculating phase operator Φ shift [x R ,y R ；x T ,y T ,k]The following are provided:
Φ shift [x R ,y R ；x T ,y T ,k]＝exp{-i2πk(a 1 x T +b 1 y T )}
wherein a is 1 ,b 1 And the reference point (x) is set in step 2.2 0 ,y 0 ,z 0 ) Related is a function R R (x,y,z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ,y 0 ,z 0 ) A first order coefficient term for Taylor expansion;
3.3)ψ 2 [x R ,y R ；x T ,y T ,k]multiplying by transverse phase operator Φ shift [x R ,y R ；x T ,y T ,k]And performs a transverse fast fourier transform as follows:
wherein k is x ,k y The following relationship is provided: k (k) x ＝k xT +a 1 k,k y ＝k yT +b 1 k, the wave number of the transformed space is represented by multiplying by a transverse phase operator;
3.4 For wavenumber spectrum ψ 3 [x T ,y T ；k x ,k y ,k]Performing Stokes interpolation in the longitudinal dimension, and interpolating the wavenumber spectrum ψ 4 [x R ,y R ；k x ,k y ,k z ]The relation is as follows:
wherein a is 1 ,b 1 ,c 1 And the reference point (x) is set in step 2.2 0 ,y 0 ,z 0 ) Related is a function R R (x,y,z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ,y 0 ,z 0 ) First order coefficient term of Taylor expansion, a 1 ,b 1 Has been calculated in step 3.2;
step four, multiplying the transverse inverse Fourier transform by a transverse phase compensation function to compensate the phase change caused by multiplying the transverse phase compensation function;
4.1 Calculating a transverse phase compensation function, Φ E1 [x,y,k z ]The following are provided:
wherein a is 2,3 ,b 2,3 ,α 1 ,β 1,2 And the reference point (x) is set in step 2.2 0 ,y 0 ,z 0 ) Related is a function R R (x,y,z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ,y 0 ,z 0 ) Higher order coefficient term of Taylor expansion, r 1,2 Is a function ofAt point (k) x0 ,k y0 ,k z0 ) Coefficient terms of Taylor expansion are processed;
4.2)Ψ 4 [x R ,y R ；k x ,k y ,k z ]is subjected to fast inverse Fourier transform to obtain the psi 4 [x R ,y R ；x,y,k z ]Multiplying by a transverse phase compensation function phi E1 [x,y,k z ]To compensate the phase change caused by multiplying the reference function to obtain a compensated wave number spectrum psi 5 [x R ,y R ；x,y,k z ]The process is as follows:
ψ 5 [x R ,yR；x,y,k z ]＝ψ 4 [x R ,y R ；x,y,k z ]·Φ E1 [x,y,k z ]
in the method, in the process of the application,representation for wave number k x ,k y Is an inverse fast fourier transform of (a);
fifthly, performing longitudinal inverse Fourier transform to obtain a target three-dimensional reconstruction;
5.1 For wave number spectrum ψ 5 [x R ,y R ；x,y,k z ]Performing longitudinal inverse Fourier transform to obtain a reconstruction result psi of the three-dimensional space domain 6 [x R ,y R ；x,y,z]The following are provided:
in the method, in the process of the application,representation for wave number k z Is an inverse fast fourier transform of (a);
5.2 Processing psi) 6 [x R ,y R ；x,y,z]Obtaining a final reconstruction result ρx R ,y R ；x,y,z]The following are provided:
ρ[x R ,t R ；x,y,z]＝|ψ 6 [x R ,y R ；x,y,z]| 2
the method can be realized in a non-visual field three-dimensional reconstruction system based on the analytic signal and the compensation reference function, the system comprises a processor and a memory, wherein the memory stores a computer program, and the computer program realizes the non-visual field three-dimensional reconstruction method based on the analytic signal and the compensation reference function when being executed by the processor.
The method can also be realized based on a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and when the computer program is executed by a processor, the non-visual field three-dimensional reconstruction method based on the analytic signal and the compensation reference function is realized.
The application is further described below in connection with specific embodiments.
A simulation scene as shown in fig. 3 was set, the reflection intermediate surface position z=0 was set, the number of scanning points was set to 64×64, and the scanning range (x T ,y T )∈[-0.4,0.4×[-0.4,0.4]The method comprises the steps of carrying out a first treatment on the surface of the The number of receiving points is set to 1, and the positions of the receiving points (x R ,y R ) = (-1.2, -0.4); setting a simulation scene as a Stanford rabbit; laser position (-1,0,1.73), detector position (-1,0.1,1.73); as in fig. 3, "" indicates laser position, "■" indicates detector position, "×" indicates laser scan point, "+%" indicates detector receive point;
setting the time resolution of the detector, the energy of the laser and other related parameters, generating simulation data, cutting to obtain non-visual field data, and processing according to the following steps:
step 1, data preprocessing; converting the received time-photon data into time-amplitude data, and performing Hilbert transformation to obtain an analytic signal thereof;
step 2, performing three-dimensional Fourier transform on the analysis signal, and multiplying the wave number spectrum after transformation by a compensation-reference function;
step 3, multiplying the wave number spectrum by a transverse phase operator after transverse inverse Fourier transform, and then performing longitudinal Stokes interpolation after transverse Fourier transform;
step 4, multiplying the transverse inverse Fourier transform by a transverse phase compensation function to compensate the phase change caused by multiplying the transverse phase compensation function by a compensation-reference function;
step 5, performing longitudinal inverse Fourier transform to obtain a target three-dimensional reconstruction;
the embodiment can see that the simulation environment is harsh, the position of the receiving point of the detector is far away from the object, and the existing non-visual field algorithm lacks the capability of quickly reconstructing the non-visual field data; in addition, due to the influence of actual physical factors, the part of the reconstruction target, which is close to the detection point, can contribute more energy, so that the distribution of data becomes more complex, and the part of the target object, which is far away from the detection point, is difficult to reconstruct by the traditional reconstruction algorithm;
the result of reconstruction is 64×64×512 voxel data, the total reconstruction time of the algorithm is about 11s, and the conventional back projection algorithm often needs several minutes or more to give similar results; (the implementation software adopted in the embodiment is matlab2018, and the processor is i7-7700HQ,16G memory)
The final reconstruction result is shown in fig. 4, the result shown in the 1 st figure in fig. 4 is the original non-visual field reconstruction result of the unmodified omega KA algorithm, and it can be seen that the application introduces the omega KA algorithm into the non-visual field imaging, and the reconstruction result of the troublesome non-visual field data for the traditional algorithm can be obtained rapidly, but the imaging result is compared with the model; the result shown in figure 2 of figure 4 is a non-view reconstruction result after the reference function in the original omega algorithm is modified to the compensation-reference function, and the reconstruction result is obviously clear than before by introducing the modified compensation-reference function. This is because the original qka algorithm is used in the field of synthetic aperture radars, often taking into account only the phase factor of the signal and ignoring the contribution of the signal amplitude to the final result. The improved compensation-reference function of the application aims at the characteristics of the signal in the non-vision field, and compensates the amplitude of the signal, so that the result is obviously improved; the result shown in fig. 4, 3, is a non-visual field reconstruction result based on the analysis signal and the compensation reference function, and the reconstruction result is obviously improved compared with the previous reconstruction result by processing the original data into the analysis signal and reconstructing the part of the target with insufficient reflection, namely the part of the target object far away from the detection point;
the above examples of the present application are provided for clarity of illustration only and are not intended to limit the method of practicing the application. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which are within the spirit and principle of the present application should be included in the protection scope of the present application as set forth in the claims.
Claims (7)
1. The non-visual field three-dimensional reconstruction method based on the analytic signal and the compensation reference function is characterized by comprising the following steps of:
step 1, data preprocessing;
receive time-photon data τx R ，y R ；x T ，y T ，t]Conversion to time-amplitude data ψ [ x ] R ，y R ；x T ，y T ，t]For psi [ x ] R ，y R ；x T ，y T ，t]Hilbert transform is performed to obtain psi H [x R ，y R ；x T ，y T ，t]To psi H [x R ，y R ；x T ，y T ，t]Resolving to obtain resolved signal psi A [x R ，y R ；x T ，y T ，t]The method comprises the steps of carrying out a first treatment on the surface of the Where t represents the time of arrival of the time-recorded photon, (x) R ，y R ) For receiving the point XOY spatial coordinates, (x T ，y T ) The scanning point XOY space coordinates; the XOY plane coincides with the reflective intermediate plane;
step 2, analyzing the signal psi A [x R ，y R ；x T ，y T ，t]Performing three-dimensional Fourier transform, and compensating the wave number spectrum after transformation by using a compensation-reference function;
step 2.1, analyzing the signal ψ A [x R ，y R ；x T ，y T ，t]Performing three-dimensional Fourier transform to obtain a wave number spectrum psi after transformation 1 [x R ，y R ；k xT ，k yT ，k]；k xT ，k yT K represents x T ，y T T is the wave number domain, k corresponding to the three-dimensional Fourier transform xT Representing the scan abscissa x T Wave number domain, k, corresponding to three-dimensional Fourier transform yT Representing the scanning ordinate y T Three-dimensional fourierThe wave number domain corresponding to the transformed wave number domain, k represents the wave number domain corresponding to the time t after three-dimensional Fourier transform;
step 2.2, setting a reconstruction region reference point (x 0 ，y 0 ，z 0 ) And calculate the compensation-reference function phi based thereon CRFM [x R ，y R ；k xT ，k yT ，k]；
Step 2.3 wave number Spectrum ψ 1 [x R ，y R ；k xT ，k yT ，k]Multiplying the compensation-reference function phi CRFM [x R ，y R ；k xT ，k yT ，k]Obtaining wave number spectrum ψ 2 [x R ，y R ；k xT ，k yT ，k]；
Step 3, for wave number spectrum ψ 2 [x R ，y R ；k xT ，k yT ，k]Multiplying a transverse phase operator after transverse inverse Fourier transform, and then carrying out Stokes interpolation in a longitudinal dimension after transverse Fourier transform;
step 3.1, vs. wave number Spectrum ψ 2 [x R ，y R ；k xT ，k yT ，k]Performing transverse inverse Fourier transform to obtain psi 2 [x R ，y R ；x T ，y T ，k]；
Step 3.2, calculating the transverse phase operator phi shift [x R ，y R ；x T ，y T ，k]；
Step 3.3, ψ 2 [x R ，y R ；x T ，y T ，k]Multiplying by transverse phase operator Φ shift [x R ，y R ；x T ，y T ，k]And performing transverse fast Fourier transform to obtain ψ 3 [x R ，y R ；k x ，k y ，k]The method comprises the steps of carrying out a first treatment on the surface of the Wherein k is x Representing the wavenumber domain, k, corresponding to the Fourier transform of the dimension corresponding to the space abscissa x with the reference point as the center y Representing a wave number domain corresponding to the space ordinate y taking the reference point as the center after the dimension Fourier transform, and k represents a wave number domain corresponding to the space ordinate y after the time t dimension Fourier transform;
step 3.4 for wave number spectrum ψ 3 [x R ，y R ；k x ，k y ，k]Performing Stokes interpolation in the longitudinal dimension to obtain a wavenumber spectrum ψ 4 [x R ，y R ；k x ，k y ，k z ]；k z Representing a wave number domain corresponding to the space depth coordinate z taking the reference point as the center after the dimension Fourier transform;
step 4, utilizing a transverse phase compensation function to correct the psi 4 [x R ，y R ；k x ，k y ，k z ]Compensating the wave number spectrum after the transverse inverse Fourier transform;
step 4.1, calculating a transverse phase compensation function phi E1 [x，y，k z ]；
Step 4.2, pair ψ 4 [x R ，y R ；k x ，k y ，k z ]Performing fast inverse Fourier transform on the transverse dimension of (2) to obtain phi 4 [x R ，y R ；x，y，k z ]；
Step 4.3, ψ 4 [x R ，y R ；x，y，k z ]Multiplying by a transverse phase compensation function phi E1 [x，y，k z ]To compensate the phase change caused by multiplying the reference function to obtain a compensated wave number spectrum psi 5 [x R ，y R ；x，y，k z ]；
Step 5, performing longitudinal inverse Fourier transform to obtain a target three-dimensional reconstruction;
step 5.1 for wavenumber spectrum ψ 5 [x R ，y R ；x，y，k z ]Performing longitudinal inverse Fourier transform to obtain a reconstruction result psi of the three-dimensional space domain 6 [x R ，y R ；x，y，z]；
Step 5.2, processing ψ according to the following 6 [x R ，y R ；x，y，z]Obtaining a final reconstruction result ρx R ，y R ；x，y，z]；
ρ[x R ，y R ；x，y，z]＝|ψ 6 [x R ，y R ；x，y，z]| 2 。
2. The non-visual field three-dimensional reconstruction method based on the analytic signal and the compensating reference function of claim 1, wherein in step 2.2:
in the method, in the process of the application,exp {.cndot }' represents an exponential function based on a natural number e; />Amplitude term for the reference function; /> For the phase term of the compensation-reference function i represents an imaginary number.
3. The non-visual field three-dimensional reconstruction method based on the analytic signal and the compensating reference function of claim 2, wherein in step 1:
ψ A [x R ，y R ；x T ，y T ，t]＝ψ[x R ，y R ；x T ，y T ，t]+iψ H [x R ，y R ；x T ，y T ，t]
in the method, in the process of the application,representing the hilbert transform with respect to time t, i representing the imaginary number.
4. A non-visual field three-dimensional reconstruction method based on an analytic signal and a compensating reference function as claimed in claim 3, wherein in step 3.2):
Φ shift [x R ，y R ；x T ，y T ，k]＝exp{-i2πk(a 1 x T +b 1 y T )}
wherein a is 1 ，b 1 Is a function R R (x，y，z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ，y 0 ，z 0 ) A first order coefficient term for taylor expansion.
5. The method of non-visual field three-dimensional reconstruction based on analytic signal and compensating reference function of claim 4, wherein in step 3.4)
Wherein a is 1 ，b 1 ，c 1 Is a function R R (x，y，z)＝((x-x R ) 2 +(y-y R ) 2 +z 2 ) 1/2 At the point (x) 0 ，y 0 ，z 0 ) A first order coefficient term for taylor expansion.
6. The utility model provides a three-dimensional rebuilding system of non-field of view based on analytic signal and compensation reference function, includes processor and memory, stores computer program in the memory, its characterized in that: the computer program, when executed by a processor, implements the non-visual field three-dimensional reconstruction method based on an analytic signal and a compensating reference function of any one of claims 1-5.
7. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program, when executed by a processor, implements the non-visual field three-dimensional reconstruction method based on an analytic signal and a compensating reference function of any one of claims 1-5.
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