CN113406594B - Single photon laser fog penetrating method based on double-quantity estimation method - Google Patents

Abstract

The invention discloses a single photon laser fog penetrating method based on a double-quantity estimation method. Step 1: establishing a fog model based on Gamma distribution; step 2: establishing a target echo signal model; step 3: detecting total echo photons; step 4: and (3) extracting the target signal in the total echo photons detected in the step (3) through the model of the fog in the step (1) and the target echo signal model in the step (2). The method is used for solving the problem that the full parameter estimation method, the single parameter estimation method and the traditional peak value method have weak target signal extraction capability.

Description

A single-photon laser fog penetration method based on dual-quantity estimation method

Technical Field

The invention belongs to the field of Gm-APD laser radar detection, and specifically relates to a single-photon laser fog penetration method based on a dual-quantity estimation method.

Background Art

With the development of new applications such as automotive lidar and drones, there is growing interest in high-resolution imaging of targets in visually degraded environments, especially in dense fog. When the laser propagation environment is a highly scattering medium, the main limitation of active optical imaging is the absorption and scattering of the laser, which leads to significant signal attenuation within a relatively short propagation distance. When performing deep imaging in dense fog, the number of photons in the target echo is too small to extract the target signal from the dense fog signal. Therefore, it is necessary to develop an algorithm to separate the target signal from the smoke background to meet the needs of deep image detection and short-time imaging of targets behind dense outdoor smoke, and to improve the weather adaptability of Gm-APD lidar.

Traditional peak selection algorithm (PSA): The peak point of the signal in each pixel is selected as the distance position of the target.

Single parameter estimation algorithm (SPEA): According to the measured fog attenuation coefficient and the Gamma distribution model of smoke, the single parameter estimation algorithm (SPEA) is used to reconstruct the depth image.

All parameter estimation algorithm (APEA): The target signal is approximately regarded as noise, and the maximum likelihood estimation is used to directly estimate the photon distribution histogram, and then reconstruct the depth image.

Traditional peak selection algorithm (PSA): The peak selection algorithm can only extract signals from targets behind low-concentration smoke. When the smoke concentration increases, the smoke echo intensity is larger and the target echo intensity is smaller. The target peak is almost submerged in the falling edge of the smoke echo signal, and the target signal can hardly be found.

Single parameter estimation algorithm (SPEA): Due to the density, dynamics and non-uniformity of fog, it is difficult to accurately obtain its true value when measuring its attenuation coefficient. Therefore, using it for parameter estimation will result in large errors, and this scheme is not suitable for outdoor experiments.

All parameter estimation algorithm (APEA): Since the echo signal contains smoke signals and target signals, ignoring the target signal and directly estimating the parameters of the echo photon histogram will lead to large parameter estimation errors.

Summary of the invention

The present invention provides a single-photon laser fog penetration method based on a dual-quantity estimation method, which can solve the problem of weak target signal extraction capability in the above three methods, improve the smoke signal estimation accuracy of the latter two algorithms, and better extract weak target signals in extreme environments.

The present invention is achieved through the following technical solutions:

A single-photon laser fog penetration method based on a dual-quantity estimation method, the single-photon laser fog penetration method comprising the following steps:

Step 1: Establish a fog model based on Gamma distribution;

Step 2: Establish target echo signal model;

Step 3: Detect total echo photons;

Step 4: Extract the target signal in the total echo photons detected in step 3 through the fog model in step 1 and the target echo signal model in step 2.

Furthermore, the step 1 is specifically that, in the triggering of the Gm-APD detector, when the laser pulse energy is extremely weak, the background noise, dark count noise and the initial number of electrons generated by the echo photons all obey the Poisson distribution; the echo photons include the target echo, backscattering and ambient light 0; according to the Poisson distribution statistics, the probability of generating q photoelectric events in the detection interval from _t1 to _t2 is:

Where Nr(t ₁ ,t ₂ ) is the average number of photons in the detection interval from t ₁ to t ₂ , expressed as:

Where λ(t) is the rate function of the initial electrons in the GM-APD detector; the probability of not generating photoelectrons during the detection time t ₁ to t ₂ is P(0)=exp(-Nr(t ₁ ,t ₂ )), so the probability of generating photoelectrons is 1-exp(-Nr(t ₁ ,t ₂ )); since the Gm-APD detector generates only one detection within the range gate, the probability of generating a detection in the jth time slot is:

According to the detection probability distribution curve of the number of photons output by the Gm-APD detector on the time axis, the average number of photons Nr(j) arriving at the focal plane of the detector in the jth time slot can be obtained by reverse calculation, which is expressed as:

Since smoke particles have strong scattering and absorption effects on lasers, there are continuous scattering events of photons during the forward transmission of the laser. If the initial number of photons in each scattering event is N ₀ , the number of photons N(t) after one scattering changes with time satisfies the relationship:

N(t)＝N ₀ exp(-αct) (5)

Among them, α is the attenuation coefficient of laser in fog, c is the speed of light;

The probability density function of photons in a scattering event is:

其中k为散射次数；Gamma分布是用来解决从开始到k个随机事件都发生所需要的时间问题，k个独立指数随机变量的总和服从Gamma分布，T～GAMMA(k，β)；因此得到激光在烟雾中传输时回波光子数随时间t变化的密度函数：Since each scattering event is independent of each other, the detection time τ _i of each scattered photon satisfies the exponential distribution; the detection time of a photon after multiple scatterings is

Where k is the number of scattering times; Gamma distribution is used to solve the time problem from the beginning to the occurrence of k random events. The sum of k independent exponential random variables obeys the Gamma distribution, T~GAMMA(k,β); therefore, the density function of the number of echo photons changing with time t when the laser is transmitted in smoke is obtained:

Where Г(k) is the Gamma function, k and β are the shape and inverse scale parameters; when k = 1, the Gamma distribution is an exponential distribution:

G _T (t|k＝1,β)＝βexp(-βt) (8)

Let β = αc, and use formula (4) (6) to calculate that the number of photons reaching the focal plane of the detector after continuous scattering by smoke is:

where r is related to the backscatter coefficient of the smoke.

Furthermore, the step 2 is specifically to use the Gaussian function as a fitting model of the target echo signal, and the fitting model is expressed as:

Among them, the center position t _target is related to the target distance, t _target = 2d/c, where d is the target distance; FWHM is introduced into the model to characterize the characteristics of the echo signal; the FWHM after the laser emission pulse interacts with the target surface is τ _p , τ _p is proportional to σ, and is obtained by the following formula:

The photon distribution of the target signal photon at time t is obtained from formulas (11)-(13):

Where s is related to the backscatter coefficient of the target.

Furthermore, the step 3 is specifically as follows: since the smoke is close to the radar system and has a high concentration, the intensity of its echo signal is greater than the intensity of the target signal, the detected echo signal has a bimodal distribution, and the target signal echo peak exists at the falling edge of the smoke signal; the number of echo photons detected at time t is as follows:

Furthermore, the step 4 specifically includes the following steps:

Step 4.1: Estimation of the time profile of the echo signal;

Step 4.2: Determine the fog signal location based on the time profile estimation in step 4.1;

Step 4.3: Based on the fog signal position in step 4.2, perform smoke signal estimation;

Step 4.4: Based on the smoke signal estimation in step 4.3, perform target signal estimation.

Furthermore, step 4.1 is as follows: each pixel of the photon counting radar records the flight time of the received photon, thereby obtaining a flight time histogram of the echo photon, obtaining the detection probability in each time bin according to the number of imaging frames, and then calculating the photon distribution Nf(t) arriving at the focal plane of the detector by formula (4), and then filtering with a Gaussian function to obtain a time profile estimate.

Furthermore, the step 4.2 specifically includes estimating the peak positions of the smoke and target echo signals; performing target and smoke peak detection on the estimated time profile signal using continuous wavelet transformation;

The continuous wavelet transform formula is as follows:

是母小波，p和q是缩放因子和移位因子，

是缩放和平移小波。Where CoC _s is the CWT coefficient, s(t) is the signal obtained by Gaussian fitting,

is the mother wavelet, p and q are the scaling factor and shift factor,

is a scaled and translated wavelet.

Furthermore, the step 4.3 is specifically to use the calculated N _f (t) to estimate the parameters of _GT (t|k,β); the smoke signal estimation mainly includes the following steps:

Step 4.3.1: Obtain the starting position τ _a and the ending position τ _b of the smoke echo signal according to the CWT transformation, and extract the number of echo photons within the range τ _a to τ _b to obtain N _f (τ _ab );

Step 4.3.2: Normalize N _f (τ _ab ) in step 4.3.1 and calculate its mean E(τ _ab ) and variance D(τ _ab ). From the GAMMA distribution function, if t～GAMMA(k, β), the mean and variance are E(t)＝k/β, D(t)＝k/β ² . Therefore, β＝E(τ _ab )/D(τ _ab ) in time τ _a to τ _b ;

Step 4.3.3: Based on β obtained in step 4.3.2, use maximum likelihood estimation to obtain the estimated value of the distribution parameter k, and finally obtain the estimated smoke echo signal distribution _GT (t|k,β);

Step 4.3.4: The peak intensity and position of the smoke echo signal N _f (τ _ab ) obtained by CWT are scaled to _GT (t|k,β) obtained in step 4.3.3 according to the maximum value of N _f (τ _ab ). The scale of change is r in formula (9). After peak shift, the smoke echo signal G _Tr (t|k,β) is obtained.

Furthermore, the step 4.4 is specifically as follows: subtract the calculated total echo photon number N _f (t) from the estimated smoke signal G _Tr (t|k, β) to obtain the initial photon number distribution S _T (t) of the target signal; fit the reflected echo signal after the laser emission pulse interacts with the target surface to obtain FWHM τ _p , and then obtain the Gaussian system response function R according to formula (14); extract the depth information of the target from the histogram of each pixel using the cross-correlation method; for each pixel, the cross-correlation coefficient C _r (t) is calculated by the histogram S _T (t) of the target echo and the system response function R of each pixel, and the expression is as follows:

The maximum point in the calculation result Cr(t) is the distance position of the target;

By estimating the distance of the target in each pixel, the depth image of the entire target is finally obtained.

The beneficial effects of the present invention are: (advantages, the more the better)

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a standard image of a target without smoke.

FIG2 is a histogram distribution diagram of a standard image of a target without smoke.

FIG3 is a diagram showing the location distribution of the experimental scene and targets of the present invention.

FIG4 is a diagram showing the target single pixel echo signal distribution and signal extraction under different attenuation coefficients.

Figure 5 is a comparison diagram of the target depth image reconstruction results under different attenuation lengths, among which (a) is a target signal extraction diagram using the peak method to estimate the time profile, (b) is a smoke echo signal diagram estimated based on the measured attenuation length value, (c) is a smoke echo signal diagram estimated based on the measured photon flight time histogram raw data, and (d) is a target signal diagram extracted by the present invention.

Figure 6 is a comparison of the target depth image reconstruction results under different acquisition times, where F represents the acquisition frame number. (a) is a comparison chart of the acquisition frame numbers of 3000, 7500, 12500 and 17500 when the time profile is estimated using the peak method, (b), (c), (d)

Figure 7 is a comparison of the evaluation indicators of the depth image reconstruction results under different acquisition frame numbers, among which (a) is a curve diagram of the TR of the reconstructed image changing with the acquisition frame number when AL=1.2, (b) is a curve diagram of the RARE of the reconstructed image changing with the acquisition frame number when AL=1.2, (c) is a curve diagram of the RARE of the reconstructed image changing with the acquisition frame number when AL=3.6, and (d) is a curve diagram of the TR of the reconstructed image changing with the acquisition frame number when AL=3.6.

Figure 8 is a histogram distribution diagram of images reconstructed by different algorithms under a small number of acquisition frames, where (a) the attenuation length AL = 1.2, F = 3000, A, B and Background correspond to the position map of targets A, B and background in the standard image respectively, and (b) the attenuation length AL = 2.7, F = 3000, A, B and Background correspond to the position map of targets A, B and background in the standard image respectively.

FIG9 is a flow chart of the method of the present invention.

DETAILED DESCRIPTION

The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

A single-photon laser fog penetration method based on a dual-quantity estimation method, the single-photon laser fog penetration method comprising the following steps:

Step 1: Establish a fog model based on Gamma distribution;

Step 2: Establish target echo signal model;

Step 3: Detect total echo photons;

Step 4: Extract the target signal in the total echo photons detected in step 3 through the fog model in step 1 and the target echo signal model in step 2.

Furthermore, the step 1 is specifically that the pulse laser radar based on the Gm-APD detector measures the distance of the target by the photon flight time method. As an important component of the photon counting radar, the laser emits a periodic light beam to the target, and starts the time digital converter (TDC) to start timing. When the echo pulse is received, the TDC is triggered to stop timing, and the target distance is obtained by the flight time recorded by the TDC; in the triggering of the Gm-APD detector, when the laser pulse energy is extremely weak, the background noise, dark count noise and the initial number of electrons generated by the echo photons all obey the Poisson distribution; the echo photons include target echo, backscatter and ambient light 0; according to the Poisson distribution statistics, the probability of generating q photoelectric events in the detection interval from _t1 to _t2 is:

Where Nr(t ₁ ,t ₂ ) is the average number of photons in the detection interval from t ₁ to t ₂ , expressed as:

Where λ(t) is the rate function of the initial electrons in the GM-APD detector; the probability of not generating photoelectrons during the detection time t ₁ to t ₂ is P(0)=exp(-Nr(t ₁ ,t ₂ )), so the probability of generating photoelectrons is 1-exp(-Nr(t ₁ ,t ₂ )); since the Gm-APD detector generates only one detection within the range gate, the probability of generating a detection in the jth time slot is:

According to the detection probability distribution curve of the number of photons output by the Gm-APD detector on the time axis, the average number of photons Nr(j) arriving at the focal plane of the detector in the jth time slot can be obtained by reverse calculation, which is expressed as:

Since smoke particles have strong scattering and absorption effects on lasers, there are continuous scattering events of photons during the forward transmission of the laser. If the initial number of photons in each scattering event is N ₀ , the number of photons N(t) after one scattering changes with time satisfies the relationship:

N(t)＝N ₀ exp(-αct) (5)

Among them, α is the attenuation coefficient of laser in fog, c is the speed of light;

The probability density function of photons in a scattering event is:

其中k为散射次数；Gamma分布是用来解决从开始到k个随机事件都发生所需要的时间问题，k个独立指数随机变量的总和服从Gamma分布，T～GAMMA(k，β)；因此得到激光在烟雾中传输时回波光子数随时间t变化的密度函数：Since each scattering event is independent of each other, the detection time τ _i of each scattered photon satisfies the exponential distribution; the detection time of a photon after multiple scatterings is

Where k is the number of scattering times; Gamma distribution is used to solve the time problem from the beginning to the occurrence of k random events. The sum of k independent exponential random variables obeys the Gamma distribution, T~GAMMA(k,β); therefore, the density function of the number of echo photons changing with time t when the laser is transmitted in smoke is obtained:

Where Г(k) is the Gamma function, k and β are the shape and inverse scale parameters; when k = 1, the Gamma distribution is an exponential distribution:

G _T (t|k＝1,β)＝βexp(-βt) (8)

Let β = αc, and use formula (4) (6) to calculate that the number of photons reaching the focal plane of the detector after continuous scattering by smoke is:

where r is related to the backscatter coefficient of the smoke.

Furthermore, the step 2 is specifically as follows: since the received echo signal is the convolution result of the laser emission pulse and the target surface reflection signal intensity at different distances, and the emission pulse and target surface reflection signal of most radar systems approximately satisfy the Gaussian distribution; the Gaussian function is used as the fitting model of the target echo signal, and the fitting model is expressed as:

Among them, the center position t _target is related to the target distance, t _target = 2d/c, where d is the target distance; since the FWHM parameter of the echo signal reflects the surface roughness, some other surface geometric characteristics and the width of the emission pulse; FWHM is introduced into the model to characterize the characteristics of the echo signal; the FWHM after the laser emission pulse interacts with the target surface is τ _p , τ _p is proportional to σ, and is obtained by the following formula:

The photon distribution of the target signal photon at time t is obtained from formulas (11)-(13):

Where s is related to the backscatter coefficient of the target.

Furthermore, step 3 is specifically to consider the application scenario of the laser radar system where smoke exists between the target and the system, and the smoke concentration is relatively high, in a nonlinear, non-steady-state state. The echo photons mainly include smoke echo photons, target echo photons and noise photons; the noise intensity is extremely weak compared to the smoke intensity, so the model of the present invention does not consider noise photons; because the smoke is close to the radar system and has a high concentration, its echo signal intensity is greater than the target signal intensity, the detected echo signal has a bimodal distribution, and the target signal echo peak exists on the falling edge of the smoke signal; the number of echo photons detected at time t is as follows:

Furthermore, since each pixel of the area array photon counting radar has time resolution capability, the echo signal in each pixel includes smoke backscattered light and signal light, and our goal is to separate the target signal from the smoke background signal. The step 4 specifically includes the following steps:

Step 4.1: Estimation of the time profile of the echo signal;

Step 4.2: Determine the fog signal location based on the time profile estimation in step 4.1;

Step 4.3: Based on the fog signal position in step 4.2, perform smoke signal estimation;

Step 4.4: Based on the smoke signal estimation in step 4.3, perform target signal estimation.

Furthermore, step 4.1 is as follows: each pixel of the photon counting radar records the flight time of the received photon, thereby obtaining a flight time histogram of the echo photon, obtaining the detection probability in each time bin according to the number of imaging frames, and then calculating the photon distribution Nf(t) arriving at the focal plane of the detector by formula (4), and then filtering with a Gaussian function to obtain a time profile estimate.

Furthermore, the step 4.2 is specifically that, due to the small distance between the target and the smoke, there is a phenomenon of overlapping peaks in the echo signal. In order to separate the target signal from the background smoke signal, the peak positions of the smoke and target echo signals are estimated; wavelet transform, as a signal analysis tool, has achieved great success in peak detection; continuous wavelet transform (CWT) can detect the number and position of the components of the full waveform echo signal of the lidar. Therefore, the peaks of the target and smoke are detected by using continuous wavelet transform on the estimated time contour signal;

The continuous wavelet transform formula is as follows:

是母小波，p和q是缩放因子和移位因子，

是缩放和平移小波。Where CoC _s is the CWT coefficient, s(t) is the signal obtained by Gaussian fitting,

is the mother wavelet, p and q are the scaling factor and shift factor,

is a scaled and translated wavelet.

Furthermore, the step 4.3 is specifically that the number of echo photons after the laser passes through the smoke satisfies the Gamma distribution over time t, therefore, the calculated N _f (t) is used to estimate the parameters of _GT (t|k, β); since N _f (t) contains smoke echo and target echo information, ignoring the target signal and directly estimating the parameters of N _f (t) will result in a large error in parameter estimation. In order to improve the accuracy of _GT (t|k, β) parameter estimation, only the smoke echo signal is calculated during parameter estimation. The smoke signal estimation mainly includes the following steps:

Step 4.3.1: Obtain the starting position τ _a and the ending position τ _b of the smoke echo signal according to the CWT transformation, and extract the number of echo photons within the range τ _a to τ _b to obtain N _f (τ _ab );

Step 4.3.2: Normalize N _f (τ _ab ) in step 4.3.1 and calculate its mean E(τ _ab ) and variance D(τ _ab ). From the GAMMA distribution function, if t～GAMMA(k, β), the mean and variance are E(t)＝k/β, D(t)＝k/β ² . Therefore, β＝E(τ _ab )/D(τ _ab ) in time τ _a to τ _b ;

Step 4.3.3: Based on β obtained in step 4.3.2, use maximum likelihood estimation to obtain the estimated value of the distribution parameter k, and finally obtain the estimated smoke echo signal distribution _GT (t|k,β);

Step 4.3.4: The peak intensity and position of the smoke echo signal N _f (τ _ab ) obtained by CWT are scaled to _GT (t|k, β) obtained in step 4.3.3 according to the maximum value of N _f (τ _ab ). The scale of change is r in formula (9). After peak shift, the smoke echo signal G _Tr (t|k, β) is obtained.

Furthermore, the step 4.4 is specifically as follows: subtract the calculated total echo photon number N _f (t) from the estimated smoke signal G _Tr (t|k, β) to obtain the initial photon number distribution S _T (t) of the target signal; due to factors such as the non-steady state of smoke distribution and the instability of the system, the target echo photons S _T (t) of each pixel point are non-uniformly distributed. The reflected echo signal after the laser emission pulse interacts with the target surface is fitted to obtain FWHMτ _p , and then the Gaussian system response function R is obtained according to formula (14); the cross-correlation method is used to extract the depth information of the target from the histogram of each pixel; for each pixel, the cross-correlation coefficient C _r (t) is calculated by the histogram of the target echo S _T (t) and the system response function R of each pixel, and the expression is as follows:

The maximum point in the calculation result Cr(t) is the distance position of the target;

By estimating the distance of the target in each pixel, the depth image of the entire target is finally obtained.

In order to test the stability of the radar system, it is necessary to image the target without smoke before the experiment begins, and analyze whether the histogram of the echo signal meets the experimental requirements. The imaging results are shown in Figure 1. The contour information of targets A and B is consistent with the actual target situation in Figure 3, and is completely separated from the background. The histogram result of Figure 1 is shown in Figure 2. The horizontal axis is the photon flight time, one time bin represents 1ns, and the vertical axis is the number of photons in the time bin. The curve mainly includes three peaks, among which the first peak and the second peak differ by 3 time bins, that is, 3ns. According to the speed of the laser in the air of about 3×10 ⁸ m/s, it can be calculated that the distance between the two peaks ΔL ₁ =3×10 ^-9 ×3×10 ⁸ /2=0.45m, the first peak and the third peak differ by 38 time bins, and the difference distance ΔL ₂ is about 5.7m. The distance between the calculated results ΔL ₁ and ΔL ₂ and the actual targets A and B is equal to the distance between target A and the background plate. Due to the time jitter of the laser and detector and other instruments, the measured target position differs from the actual position by 3 time bins, but the relative position of the target is consistent with the actual situation. Therefore, the measurement results of the system meet the experimental requirements. The present invention uses Figure 1 as a standard image for judging the subsequent smoke image processing results. Figure 2 is the histogram distribution of the standard image, and the three peaks are represented as target A, target B and background plate respectively. Figure 3 is the experimental scene and the position distribution of the target.

In order to test the ability of our algorithm to extract weak target signals through smoke, the system images target B for 20,000 frames. A pixel point within the target range is selected to obtain the target echo signal when the attenuation coefficient AL increases from 1.2 to 3.6, and the smoke and target signals are extracted according to the target signal extraction algorithm in Section 3. The results are shown in Figure 4. The red dotted line is the fitted smoke signal and the green solid line is the target signal. As the attenuation coefficient increases, the number of photons passing through the smoke decreases due to the increase in the backscattering ability of the smoke to the laser, the intensity of the smoke echo signal gradually increases, the target echo signal gradually decreases, the superimposed echo signal _FT (t) changes from a double peak to a single peak distribution, and the echo pulse width gradually decreases. When the attenuation coefficient AL = 3.6, the target signal has been completely masked by the smoke signal. The SBR value at this time is -23.2dB, which is 16.9dB less than when AL = 1.2, but our algorithm can still extract weak target signals.

Figure 4 Distribution of target single pixel echo signal and signal extraction under different attenuation coefficients. Histogram: The calculated histogram of initial reflected photons. Gaussianfit: Signal curve fitting obtained by Gaussian fitting. Gammafit: Background signal estimation. Signal: The difference between the histogram and the Gamma fit, that is, the extracted target signal photons. Target: Target signal estimation. Modelfit: The sum of the Gamma fit and the target signal.

The system continuously images targets A and B at different attenuation lengths for 20,000 frames, and the corresponding acquisition time is 1s. Different algorithms are used to extract target signals, and the reconstructed target depth image is shown in Figure 5. As the attenuation length AL increases from 1.2 to 3.6, the interference ability of smoke on the target signal gradually increases, resulting in the TR value of the target depth image reconstructed by the four algorithms becoming smaller and smaller, and the RARE value becoming larger and larger. Among them, the TR values of the images reconstructed by PSA, SPEA, APEA and the method of the present invention are reduced by 99.3%, 86.9%, 48.1% and 65.4%, respectively. Although the percentage of the TR value reduction of the method of the present invention is 17.3% greater than that of the APEA algorithm, it is reduced by 33.9% and 21.5% relative to PSA and SPEA, respectively. When AL=3.6, the TR obtained by the method of the present invention is increased by 0.2300 and 0.0408, respectively, and the RARE is reduced by 0.3793 and 0.0231, respectively, relative to SPEA and APEA, and the restored target contour is more complete and the extracted target position is more accurate. Therefore, the method of the present invention has good stability and target signal extraction capability when the attenuation length changes.

Figure 5 compares the reconstruction results of target depth images under different attenuation lengths. Different columns show the reconstruction results of different algorithms under the same attenuation length, and different rows show the reconstruction results of the same algorithm under different attenuation lengths. TR is the target recovery degree, and RARE is the relative average ranging error. (a) is the target signal extraction by using the peak method to estimate the time profile. (b) is the estimation of the smoke echo signal based on the measured attenuation length value. (c) is the smoke echo signal estimated based on the measured photon flight time histogram raw data. (d) is the target signal extracted by the method of the present invention.

When the attenuation length AL = 1.2, the target is imaged continuously in multiple frames, and the acquisition frame numbers F are 3000, 7500, 12500 and 17500 respectively, and the corresponding acquisition times are 0.150s, 0.375s, 0.625s and 0.875s respectively. Different algorithms are used to extract the target signal, and the reconstructed target depth image is shown in Figure 6. Although the depth image reconstructed by the method of the present invention has more noise than SPEA and APEA when F = 3000, the obtained TR is improved by 0.2361 and 0.2583 respectively, and the RARE is reduced by 0.1299 and 0.1137 respectively. As the acquisition time increases, the target contour reconstructed by the method of the present invention gradually becomes complete, while the SPEA and APEA algorithms are the opposite. Therefore, the method of the present invention has the best target recovery ability under a shorter acquisition time.

In order to study the influence of acquisition time on the reconstruction result of target depth image, the present invention extracts target signals from images with attenuation lengths AL of 1.2 and 3.6 respectively. The number of imaging frames increases from 3000 to 20000. The curves of TR and RARE of reconstructed images with acquisition frame number are shown in Figure 5. When the smoke concentration is low (AL = 1.2), as the number of acquisition frames increases, the TR of the images reconstructed by the four algorithms gradually increases, and the RARE gradually decreases. Compared with the SPEA and APES algorithms, the TR of the images reconstructed by the method of the present invention increases by an average of 0.3271 and 0.3327, respectively, and the RARE decreases by an average of 0.1356 and 0.1146, respectively. When the smoke concentration is high (AL = 3.6), as the number of acquisition frames increases, the TR of the images reconstructed by APEA and the method of the present invention gradually increases, while the TR of SPEA increases first and then decreases, and its value is close to zero. Although the RARE value obtained by the method of the present invention is almost equal to that of the APEA algorithm, the TR increases by an average of 0.0613. In summary, the method of the present invention has the largest TR value and the smallest RARE value, that is, when the method of the present invention reconstructs the depth image of a target with a high scattering medium or a very short acquisition time, it has good stability and target signal extraction capability.

Figure 7 Comparison of evaluation indicators of depth image reconstruction results under different acquisition frame numbers. (a) and (b) are the curves of TR and RARE of the reconstructed image with the acquisition frame number when AL=1.2, and (c) and (d) are the curves of TR and RARE of the reconstructed image with the acquisition frame number when AL=3.6.

The purpose of reconstructing the target depth image is to distinguish the targets in the image according to the distance position. Therefore, the present invention performs histogram statistics on the reconstructed target depth image under a small number of acquisition frames, and the result is shown in Figure 8. When the smoke attenuation length AL = 1.2 or AL = 2.7, the target distance values obtained by the APEA and SPEA algorithms are quite different from the target distance values of the standard image, but the histogram of the target depth image reconstructed by the method of the present invention is consistent with the standard image and contains three echo peaks. The peak method is used to search the target for the histograms of the three algorithms, and the distance errors between the targets A, B and the background in the reconstructed image and the real target are obtained, as shown in Table 1. When the attenuation length AL = 1.2 or 2.7, the average error of the method of the present invention is 0.33Bin, which is at least 4Bins higher than the traditional algorithm. The results show that the method of the present invention can distinguish multiple targets by distance value when the smoke is dense or the acquisition time is short, and has the highest sensitivity while having the highest ranging accuracy.

Figure 8. Histogram distribution of images reconstructed by different algorithms under a small number of acquisition frames, where A, B, and Background correspond to the positions of targets A, B, and background in the standard image, respectively. (a) Attenuation length AL = 1.2, F = 3000, (b) Attenuation length AL = 2.7, F = 3000.

Table 1 Comparison of the error between the target distance reconstructed by different algorithms and the actual distance

Claims (5)

1. A single-photon laser fog penetration method based on a dual-quantity estimation method, characterized in that the single-photon laser fog penetration method comprises the following steps: Step 1: Establish a fog model based on Gamma distribution; Step 2: Establish target echo signal model; Step 3: Detect total echo photons; Step 4: extract the target signal in the total echo photons detected in step 3 through the fog model in step 1 and the target echo signal model in step 2; Specifically, step 1 is as follows: in the triggering of the Gm-APD detector, when the laser pulse energy is extremely weak, the background noise, dark count noise and the initial number of electrons generated by the echo photons all obey the Poisson distribution; the echo photons include the target echo, backscattering and ambient light 0; according to the Poisson distribution statistics, the probability of generating q photoelectric events in the detection interval from _t1 to _t2 is:

Where Nr(t ₁ ,t ₂ ) is the average number of photons in the detection interval from t ₁ to t ₂ , expressed as:

Where λ(t) is the rate function of the initial electrons in the GM-APD detector; the probability of not generating photoelectrons during the detection time t ₁ to t ₂ is P(0)=exp(-Nr(t ₁ ,t ₂ )), so the probability of generating photoelectrons is 1-exp(-Nr(t ₁ ,t ₂ )); since the Gm-APD detector generates only one detection within the range gate, the probability of generating a detection in the jth time slot is:

According to the detection probability distribution curve of the number of photons output by the Gm-APD detector on the time axis, the average number of photons Nr(j) arriving at the focal plane of the detector in the jth time slot can be obtained by reverse calculation, which is expressed as:

Since smoke particles have strong scattering and absorption effects on lasers, there are continuous scattering events of photons during the forward transmission of the laser. If the initial number of photons in each scattering event is N ₀ , the number of photons N(t) after one scattering changes with time satisfies the relationship: N(t)＝N ₀ exp(-αct) (5) Among them, α is the attenuation coefficient of laser in fog, c is the speed of light; The probability density function of photons in a scattering event is:

Since each scattering event is independent of each other, the detection time τ _i of each scattered photon satisfies the exponential distribution; the detection time of a photon after multiple scatterings is

Where k is the number of scattering times; Gamma distribution is used to solve the time problem from the beginning to the occurrence of k random events. The sum of k independent exponential random variables obeys the Gamma distribution, T~GAMMA(k,β); therefore, the density function of the number of echo photons changing with time t when the laser is transmitted in smoke is obtained:

Where Г(k) is the Gamma function, k and β are the shape and inverse scale parameters; when k = 1, the Gamma distribution is an exponential distribution: G _T (t|k＝1,β)＝βexp(-βt) (8) Let β = αc, and use formula (4) (6) to calculate that the number of photons reaching the focal plane of the detector after continuous scattering by smoke is:

Where r is related to the backscattering coefficient of smoke; The step 4 specifically comprises the following steps: Step 4.1: Estimation of the time profile of the echo signal; Step 4.2: Determine the fog signal location based on the time profile estimation in step 4.1; Step 4.3: Based on the fog signal position in step 4.2, perform smoke signal estimation; Step 4.4: Based on the smoke signal estimation in step 4.3, target signal estimation is performed; The step 4.2 specifically includes estimating the peak positions of smoke and target echo signals; performing target and smoke peak detection on the estimated time profile signal using continuous wavelet transformation; The continuous wavelet transform formula is as follows:

Where CoC _s is the CWT coefficient, s(t) is the signal obtained by Gaussian fitting,

is the mother wavelet, p and q are the scaling factor and shift factor,

is a scaled and translated wavelet; Specifically, step 4.3 uses the calculated N _f (t) to estimate the parameters of _GT (t|k,β). The smoke signal estimation mainly includes the following steps: Step 4.3.1: Obtain the starting position of the smoke echo signal based on CWT transformation

and end position

, the range

to

The number of echo photons in _the

); Step 4.3.2: Substitute the N _f (

) is normalized and its mean value E(

) and variance D(

); From the GAMMA distribution function, we know that if t～GAMMA(k,β), the mean and variance are E(t)＝k/β, D(t)＝k/β ² respectively; therefore, at time

to

β = E(

)/D(

); Step 4.3.3: Based on β obtained in step 4.3.2, use maximum likelihood estimation to obtain the estimated value of the distribution parameter k, and finally obtain the estimated smoke echo signal distribution _GT (t|k,β); Step 4.3.4: The smoke echo signal N _f (

) peak intensity and position, and the _GT (t|k,β) obtained in step 4.3.3 is converted into _Nf (

) is scaled uniformly, and the change scale is r in formula (9). After peak shifting, the smoke echo signal G _Tr (t|k, β) is obtained. 2. According to the single-photon laser fog penetration method based on the dual-quantity estimation method in claim 1, it is characterized in that the step 2 specifically comprises taking the Gaussian function as the fitting model of the target echo signal, and the fitting model is expressed as:

Among them, the center position t _target is related to the target distance, t _target = 2d/c, where d is the target distance; FWHM is introduced into the model to characterize the characteristics of the echo signal; the FWHM after the laser emission pulse interacts with the target surface is τ _p , τ _p is proportional to σ, and is obtained by the following formula:

The photon distribution of the target signal photon at time t is obtained from formulas (11)-(13):

Where s is related to the backscatter coefficient of the target. 3. According to the single-photon laser fog penetration method based on the dual-quantity estimation method of claim 2, it is characterized in that the step 3 is specifically as follows: since the smoke is close to the radar system and has a large concentration, the intensity of its echo signal is greater than the intensity of the target signal, the detected echo signal has a bimodal distribution, and the target signal echo peak exists at the falling edge of the smoke signal; the number of echo photons detected at time t is as follows:

4. According to the single-photon laser fog penetration method based on the dual-quantity estimation method in claim 1, it is characterized in that, in step 4.1, each pixel point of the photon counting radar records the flight time of the received photon, thereby obtaining a flight time histogram of the echo photon, and obtaining the detection probability in each time bin according to the number of imaging frames, and then calculating the photon distribution N _f (t) reaching the focal plane of the detector by formula (4), and then filtering by Gaussian function to obtain the time profile estimation. 5. According to claim 1, a single-photon laser fog penetration method based on a dual-quantity estimation method is characterized in that the step 4.4 is specifically as follows: subtracting the calculated total echo photon number N _f (t) from the estimated smoke signal G _Tr (t|k, β) to obtain the initial photon number distribution S _T (t) of the target signal; fitting the reflected echo signal after the laser emission pulse interacts with the target surface to obtain FWHMτ _p , and then obtaining a Gaussian system response function R according to formula (14); extracting the depth information of the target from the histogram of each pixel by using the cross-correlation method; for each pixel, the cross-correlation coefficient C _r (t) is calculated by the histogram S _T (t) of the target echo and the system response function R of each pixel, and the expression is as follows:

The maximum point in the calculation result Cr(t) is the distance position of the target; By estimating the distance of the target in each pixel, the depth image of the entire target is finally obtained.

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