CN104155658A - Image reconstruction method of laser radar imaging system based on compressed sensing - Google Patents

Abstract

The invention discloses an image reconstruction method of a lidar imaging system based on compressed sensing. The laser radar imaging system of this method adopts the unit avalanche diode APD, which effectively breaks through the bottleneck problem that the current domestic linear array avalanche diode cannot be integrated on a large scale. The system consists of a laser emitting module, a telescope imaging module, a digital micromirror DMD and a control module, an avalanche diode APD, a synchronization module, a data acquisition module, and an image reconstruction module. The invention emits pulsed lasers to the target through the laser emitting module, and the reflected echoes of targets at different distances are modulated by the digital micro-mirror DMD, and then the unit avalanche diode APD is sampled in time series through the converging lens, and finally the subsequent image reconstruction is adopted The method reconstructs the 3D image of the target. The invention has the advantages of no need for any scanning, simple structure, small amount of data required for image reconstruction, and high detection sensitivity.

Description

An Image Reconstruction Method for LiDAR Imaging System Based on Compressed Sensing

technical field

The invention relates to computational imaging technology and image reconstruction algorithm, signal processing and laser radar. In particular, it relates to an image reconstruction method of a lidar imaging system based on compressed sensing.

Background technique

Lidar is an active photoelectric imaging technology. Compared with ordinary passive optical remote sensing detection and microwave radar, it has high resolution, good concealment, strong anti-interference ability, etc.; it can detect real objects through clouds, vegetation, etc. ground terrain. LiDAR transmits pulsed laser signals to the target, and then processes the received signal (echo signal) reflected from the target and the transmitted signal, so that relevant information of the target can be extracted, such as target distance, orientation, and attitude. , shape and other parameters. Using this kind of laser radar, in the military, it is possible to track, detect and identify enemy aircraft and missiles, so as to achieve precise strikes. At present, it has become an indispensable technical means in the military field of our country.

Traditional laser radar can be divided into point-by-point scanning swing-broom type and linear array push-broom type according to the working mode. The swing-sweep lidar is very mature in technology, and its biggest advantage is that the principle is very simple. But it also has great shortcomings, such as it is difficult to capture high-speed moving targets; due to the existence of mechanical scanning devices, it is difficult to achieve miniaturization and light weight; a large amount of point cloud data will affect the data transmission and storage of the data acquisition system and subsequent processing Bring great pressure; in addition, the principle of point-by-point scanning, and the limitation of flight speed and scanning speed will lead to low spatial resolution of distance images. Linear array push-broom lidar adopts the parallel detection principle of emitting multiple laser beams and multiple detectors at the same time, thereby improving coverage efficiency and scanning efficiency, and overcoming some shortcomings of point-by-point scanning lidar. At present, the research on push-broom lidar in my country is just in its infancy. However, it is difficult to achieve large-scale integration of linear array avalanche diode APD detectors. As far as the current technical means are concerned, only 25-50 units of APDs can be achieved. The process bottleneck of linear array APDs will largely hinder Development of pushbroom lidar.

Compressive sensing (Compressive Sensing, CS) is a theory that sampling and compression are performed simultaneously by Donoho and Candes, a mathematician at Stanford University in the United States (see documents 1, 2, 3) in 2006. This theory excavates the redundancy and sparsity of signal information. In the sampling process, instead of obtaining all pixel samples of the image, it selects the appropriate modulation template through a specific algorithm, that is, the observation matrix. Global samples are then used to restore the image through these samples combined with related restoration algorithms. Different from the traditional "sampling first, then compression", the CS theory is a "sampling while compression" method. Applying CS to the lidar imaging system can significantly save the number of sensors. This "sampling while compression" method The technical burden of signal processing is transferred from the sensor to the data processing. Therefore, based on the compressed sensing theory, the development of a new type of laser radar imaging system naturally becomes the research content of the present invention.

references:

[1] Donoho D L. Compressed sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

[2] Candès E, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information [J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

[3] Candès E. Compressive sampling [C]. International Congress of Mathematics, 2006: 1433-1452.

Contents of the invention

The purpose of the present invention is to provide an image reconstruction method based on a compressive sensing lidar imaging system. In terms of detectors, the unit avalanche diode APD detector is used to overcome the shortcomings of the traditional point-by-point scanning lidar and avoid the bottleneck of the linear array APD technology. In terms of data acquisition, based on the theory of compressed sensing, a small amount of data can be used to reconstruct the 3D image of the target, and the data is compressed during the sampling process, which eases the collection, transmission, and processing of large amounts of data in traditional lidar imaging. Storage pressure.

The solution proposed by the present invention is as follows:

As shown in Figure 1, the new lidar imaging system includes: laser emission module 1; telescope imaging module 2; digital micro-mirror DMD and control module 3; optical convergence lens 4; avalanche diode APD5; data acquisition module 6; Construction module 7; Synchronization module 8. It is characterized in that: the laser emission module 1 adopts a pulsed laser with a wavelength of 1064nm, its repetition frequency is 100Hz, and the pulse energy is 200mJ; the telescope imaging module 2 adopts a telescope with a focal length of 304.8mm and an aperture of 101.6mm; the digital microreflector DMD and the control module The digital micromirror DMD in 3 adopts a DMD with 1024×768 pixels and a pixel size of 13.69 μm; the focal length of the optical converging lens 4 is 10 cm; the pixel size of the avalanche diode APD5 is 1.5 mm, the dark current is 7 nA, and the rise time is 5 ns; the data The acquisition card quantization digit that acquisition module 6 adopts is 10, and sampling rate is 5GSPS; Synchronization module 8 adopts FPGA chip to generate three synchronous signals;

The workflow between the various modules of the system is as follows:

The synchronization module 8 transmits a synchronization signal to the laser emission module 1 and the digital micro-mirror DMD and the control module 3. After the laser emission module 1 receives the synchronization signal, it starts to emit pulsed laser light to the scene target. The reflected echo signals are sequentially recorded as: x ¹ , x ² ... x ^k ;

The digital micromirror DMD and the control module 3 also receive the synchronization signal at the same time, then load a modulation template and send it to the DMD, and the total number of modulation templates is set to M. The modulation template during the Mth modulation is recorded as: θ _M , the specific value is a pre-set m×n order matrix, the value of the matrix elements is 0 or 1, and all elements obey the Gaussian random distribution. Change the flip state of the DMD micromirror by modulating the template, so as to achieve the effect of modulating the target echo. In fact, θ _M is the observation matrix in compressed sensing theory, and the value range of M is is the sparsity of signal x ¹ ;

The echo signal modulated by the DMD is converged by the optical converging lens 4 to the avalanche diode APD5. In each modulation process of DMD, the target echo signals at different distances arrive at the APD at different times, and the time is recorded as: Therefore, the signal detected on the APD detector will eventually have multiple peaks in sequence, as shown in Figure 2, each peak corresponds to a target;

After the signal detected by the avalanche diode APD5 is collected by the data acquisition module 6, in the time series , get the corresponding M sets of digital signal values in turn:

The image reconstruction module 7 processes the signal collected by the data acquisition module 6, and finally obtains a three-dimensional image of each target;

The specific implementation steps of the image reconstruction module 7 are as follows:

1) For the first target, the signal collected by the data acquisition module 6 is written as the following formula (1):

$\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Rewrite formula (1) as the following matrix equation of formula (2):

F ¹ ＝Θ·X ¹ (2)

In the above formula, F ¹ is the signal The formed M×1 matrix; Θ is an M×N matrix, the number of rows M is the number of modulation templates, the number of columns N=m×n is the total number of elements of each modulation template θ _M , and each row of Θ is It is rearranged by the corresponding modulation template θ _M ; X ¹ is an N×1 matrix; based on the theory of compressed sensing, the value of M is much smaller than N. Therefore, (2) is actually an ill-conditioned equation. Direct Solving Clearly there are infinitely many solutions. However, the theory of compressed sensing points out that as long as X ¹ is sparse, or has sparseness under the representation of some kind of orthogonal transformation, then there will be a special optimization method for solving equation (2). Sparsity means that it contains a large number of data tending to zero, and only a small number of non-zero values;

For natural scene objects, in general, it is possible to have sparsity under the representation of some orthogonal transformations. For example: Fourier transform, discrete cosine transform, etc. For X ¹ , under the discrete cosine transform, it is sparsely expressed as the following formula (3):

X ¹ =Ψ·α ¹ (3)

In the above formula, α ¹ is the sparse representation of X ¹ , which is an N×1 matrix; Ψ is the N×N order discrete cosine transform matrix;

So the formula (2) is rewritten as the following formula (4):

F ¹ =Θ·X ¹ =Θ·Ψ·α ¹ =T·α ¹ (4)

In the above formula, T is the sensing matrix of order M×N; among them, only α ¹ is unknown;

The method of image reconstruction is to solve the sparse coefficient α ¹ in formula (4). Obviously (4) is actually an ill-conditioned equation. There are infinitely many solutions to the direct solution, so it is transformed into an optimization problem of the following formula (5):

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; st</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the above formula, L ₁ represents the 1 norm, is the optimal approximate solution of α ¹ ;

The optimal solution algorithm steps of formula (5) are as follows:

Step 1: Initialize an empty matrix I=[], residual matrix R=F;

The second step: make the inner product of each column in the residual R and T respectively, and find the column with the largest inner product, take this column out and add it to the matrix I;

The third step: update the residual, R=FI · ( ^IT · I) ^-1 · ^IT · F, wherein ^IT is the transposition matrix of I ( ^IT · I) ^-1 is ( ^IT · I) the inverse matrix;

The 4th step: continuously cycle the second step and the third step in sequence, the number of cycles is C, and its value range is: C≥2M;

The fifth step: the solution obtained by the final (5) formula is the following (6) formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The finally obtained image information of the first target is expressed as the following formula (7):

${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

The two-dimensional image of the target can be obtained by rearranging the N × 1 order matrix X ¹ in (7) into an m × n order matrix;

2) For the second goal, the formula (1) in step 1) is rewritten as the following formula (8):

$\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Write formula (8) as the matrix equation of formula (9):

F ² ＝Θ·X ² (9)

The method of solving formula (9) is the same as step 1), so the image information of the second target is finally obtained as the following formula (10):

${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

3) By analogy, for the kth target, the formula (1) in step 1) is rewritten as the following formula (11):

$\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\\ {{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Write formula (11) as the matrix equation of formula (12):

F ^k ＝Θ·X ^k (12)

The method of solving formula (12) is the same as step 1), so the image information of the kth target is finally obtained as the following formula (13):

${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

The two-dimensional image of the target can be obtained by rearranging the N × 1 order matrix X ^k in the formula (13) into an m × n order matrix;

4) For the distance information of the target, the time recorded by the data acquisition module (6) is averaged to obtain the following formula (14):

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

In the above formula, T ¹ is the time information of the first target, and by analogy T ^k is the distance information of the k-th target;

Then the distance information of the target is obtained as the following formula (15):

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

In the above formula, d ¹ is the distance information of the first target, and d ^k is the distance information of the k-th target by analogy;

So far, according to formulas (13) and (15), the 3D image data of all targets can be obtained.

The advantages of the present invention are:

(1) The present invention uses DMD to modulate the echo signal of the target. Compared with the traditional point-by-point scanning laser radar, the mechanical scanning device is eliminated, and the laser radar system is miniaturized and lightweight, and has strong earthquake resistance. At the same time, less sampling data is required for 3D image reconstruction.

(2) The system of the present invention adopts the unit avalanche diode APD as the detector. Compared with the traditional push-broom laser radar, it will overcome the bottleneck problem that the domestic linear array large-scale avalanche diode APD cannot be integrated in the process, and solve the push-broom laser radar at the same time. Lidar has low signal-to-noise ratio and low detection sensitivity.

Description of drawings

Fig. 1 is a laser radar imaging system and method based on compressed sensing, 1 is the laser emission module; 2 is the telescope imaging module; 3 is the digital micro-mirror DMD and the control module; 4 is the optical convergence lens; 5 is the avalanche diode APD ; 6 is a data acquisition module; 7 is an image reconstruction module; 8 is a synchronization module;

Figure 2 is the signal form of the target echo received on the APD each time, where Figure (a) is the first modulation signal, and Figure (b) is the Mth modulation signal.

Detailed ways

A better example of the present invention is given below in conjunction with FIG. 1 , which is mainly described in further detail, but not used to limit the scope of the present invention.

The specific embodiment of the present invention is mainly divided into the following steps:

(1) First determine the technical parameters of the components used in each module of the system, as follows: Laser emission module 1 adopts the laser of Shanghai Brillouin Laser Technology Co., Ltd., and the technical indicators are: working wavelength 1064nm, repetition frequency 100Hz, pulse energy 200mJ; The telescope imaging module 2 adopts the telescope of Edmund Optics (Shenzhen) Co., Ltd., the selected focal length is 304.8mm, and the aperture is 101.6mm. The digital micromirror DMD and the control module 3 adopt the DMD produced by TI Company of the United States, the technical index is 1024×768 pixels, the pixel size is 13.69 μm, the control board adopts the TI-Discovery-4100 matched with it; the focal length of the optical convergence lens 4 is 10cm; avalanche diode APD5 adopts AD1500-10 produced by Pacific Silicon Sensor Company of the United States, with a pixel size of 1.5mm, dark current of 7nA, rise time of 5ns, and response rate of 36A/w; data acquisition module 6 adopts QT1230 acquisition card of Kunchi Technology, The technical indicators are: 10 quantization digits, the highest sampling rate is 5GSPS; the synchronization module 8 adopts the Spartan-6-XC6SLX9 chip of Xilinx Company to generate three synchronous signals;

(2) After the system hardware is determined, firstly, the synchronization module 8 emits a synchronization signal pulse, and the laser emitting module 1 emits a pulsed laser to the target after receiving the synchronization signal pulse.

(3) At the same time, after the digital micromirror DMD and the control module 3 receive the synchronous pulse signal, a modulation template is loaded and sent to the DMD. The modulation template is a 0,1 matrix with a size of 256×192 and subject to Gaussian random distribution, These modulation templates are generated in advance, and 5000 templates are generated in this implementation. Since the DMD selected in step (1) is 1024×768 pixels, in order to allow the DMD to be correctly identified, the size of the template actually loaded into the DMD is selected to be 1024×768, and all elements exceeding 256×192 are filled with “0”. Through modulation, the micromirror of the DMD is in a certain switch state, where "on" is represented by "1" and "off" is represented by "0" (specifically, the micromirror is flipped +12° (on) and -12° (off) )). After the state of the micromirror switch is stable, the modulation of the echo target can be realized, the light reflected by flipping -12° is discarded, and the light reflected by flipping +12° then enters the subsequent optical system. Then, the data acquisition module 6 performs data acquisition. (1) (2) (3) steps are repeated 5000 times to complete the data collection.

(4) Finally, the image reconstruction module (7) processes the sampling data to obtain a three-dimensional image of the target. For a brief description, the scene is set to have 5 objects, and the spatial resolution of each object is: 256 × 192 pixel size. To reconstruct the spatial two-dimensional information of each target, 256×192 unknowns need to be solved, and the sampled data is only 5000, which is equivalent to the data being compressed by 256×192-5000=44152 during the sampling process of the data acquisition module 6 . To reconstruct the distance information of each target, it is enough to solve 5 distance information.

Claims (1)

1. An image reconstruction method based on a compressive sensing lidar imaging system, which is based on comprising a laser emission module (1); a telescope imaging module (2); a digital micromirror DMD and a control module (3); an optical convergence lens (4); Avalanche diode APD (5); Data acquisition module (6); Image reconstruction module (7); The lidar imaging system of synchronization module (8) realizes; It is characterized in that the method is as follows: The modulation template that the control module (3) loads onto the digital micromirror DMD in turn is: θ ₁ , θ ₂ ... θ _M Where: M is the number of modulations, θ ₁ , θ ₂ ... θ _M are all m×n order Gaussian random distribution matrices; During the modulation process of each modulation template, the time sequence of the target echo signals recorded by the data acquisition module (6) in sequence at different distances is: ${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}$ Among them: k is the number of targets at different distances; The data acquisition module (6) sequentially acquires the corresponding M groups of digital signal values on the above-mentioned time series: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}}$ The above data processing steps are as follows: 1) For the first target, the signal collected by the data acquisition module (6) is written as the following formula (1): $\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ Where: x ¹ is the first target signal to be reconstructed; Rewrite formula (1) as the following matrix equation of formula (2): F ¹ ＝Θ·X ¹ (2) In the above formula, F ¹ is the signal The formed M×1 matrix; Θ is an M×N matrix, the number of rows M is the number of modulation templates, and the number of columns N=m×n is the total number of images of each modulation template θ _M , and each row of Θ is It is rearranged by the corresponding modulation template θ _M ; X ¹ is an N×1 matrix composed of x ¹ ; For X ¹ , under the discrete cosine transform, it is sparsely expressed as the following formula (3): X ¹ =Ψ·α ¹ (3) In the above formula, α ¹ is the sparse representation of X ¹ , which is an N×1 matrix; Ψ is the N×N order discrete cosine transform matrix; Then formula (2) is rewritten as formula (4) as follows: F ¹ =Θ·X ¹ =Θ·Ψ·α ¹ =T·α ¹ (4) In the above formula, T is the sensing matrix of order M×N; among them, only α ¹ is unknown; The method of image reconstruction is to solve the sparse coefficient α ¹ in formula (4), and transform it into the optimization problem of formula (5): ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\mathrm{<span\; class="notranslate">\; min</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; st</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ In the above formula, L ₁ represents the 1 norm, is the optimal approximate solution of α ¹ ; The optimal solution algorithm steps of (5) are as follows: Step 1: Initialize an empty matrix I=[], residual matrix R=F; The second step: make the inner product of each column in the residual R and T respectively, and find the column with the largest inner product, take this column out and add it to the matrix I; The third step: update the residual, R=FI · ( ^IT · I) ^-1 · ^IT · F, wherein ^IT is the transposition matrix of I ( ^IT · I) ^-1 is ( ^IT · I) the inverse matrix; The fourth step: the second step and the third step are continuously sequentially cycled, the number of cycles is C, and the value range is: C≥2M; The fifth step: the solution obtained by the final (5) formula is the following (6) formula: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ The finally obtained image information of the first target is expressed as the following formula (7): ${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ The two-dimensional image of the target can be obtained by rearranging the N × 1 order matrix X ¹ in (7) into an m × n order matrix; 2) For the second goal, the formula (1) in step 1) is rewritten as the following formula (8): $\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$ Write formula (8) as the matrix equation of formula (9): F ² ＝Θ·X ² (9) The method of solving formula (9) is the same as step 1), so the image information of the second target is finally obtained as the following formula (10): ${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$ 3) By analogy, for the kth target, the formula (1) in step 1) is rewritten as the following formula (11): $\left\{\begin{array}{c}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\\ {{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\\ <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$ Write formula (11) as the matrix equation of formula (12): F ^k ＝Θ·X ^k (12) The method of solving (12) is the same as step 1), so the image information of the kth target is finally obtained as the following (13): ${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$ The two-dimensional image of the target can be obtained by rearranging the N × 1 order matrix X ^k in the formula (13) into an m × n order matrix; 4) For the distance information of the target, the time recorded by the data acquisition module (6) is averaged to obtain the following formula (14): $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$ In the above formula, T ¹ is the time information of the first target, and by analogy T ^k is the distance information of the k-th target; Then the distance information of the target is obtained as the following formula (15): $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$ In the above formula, d ¹ is the distance information of the first target, and d ^k is the distance information of the k-th target by analogy; So far, according to formulas (13) and (15), the 3D image data of all targets can be obtained.