CN111999742A - Single-quantity estimation-based Gm-APD laser radar fog-penetrating imaging reconstruction method - Google Patents
Single-quantity estimation-based Gm-APD laser radar fog-penetrating imaging reconstruction method Download PDFInfo
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- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a reconstruction method of Gm-APD laser radar fog-penetrating imaging based on single quantity estimation. Step 1: determining the composition and distribution of imaging echoes in the foggy day, wherein the imaging echoes in the foggy day are photons received by a foggy day laser radar; step 2: obtaining a backscattering distribution model of the Gm-APD laser radar according to the foggy day imaging echo composition and distribution in the step 1; and step 3: measuring and calculating the attenuation coefficient mu in the backscattering distribution model obtained in the step 2 based on an attenuation coefficient calculation formula or a visibility empirical formula; and 4, step 4: substituting the calculated attenuation coefficient mu into the backscattering distribution model in the step 2, and carrying out maximum likelihood estimation on the backscattering distribution model substituted with the attenuation coefficient mu to obtain an estimated value of the collision times k; and 5: obtaining a target distance value R through the step 4; step 6: traversing all pixels to obtain a reconstructed three-dimensional range profile R after the backscattering of the fog is inhibitedxy. The recovery accuracy of the target in the fog is effectively improved.
Description
Technical Field
The invention belongs to the technical field of laser radars; in particular to a reconstruction method of Gm-APD laser radar fog-penetrating imaging based on single quantity estimation.
Background
At present, defogging processing for imaging in foggy days is mainly focused on an image layer, and comprises algorithms based on foggy day image enhancement, such as a homomorphic filtering algorithm, a Retinex algorithm and the like, foggy day image restoration based on a McCartney atmospheric scattering model, such as defogging processing based on a depth relation, and a defogging method which is considered to be the best defogging method at present, such as a defogging method based on dark channel prior, wherein the methods have good effects of repairing colors of all parts of an image and improving image contrast, but cannot be directly used for defogging processing of a Gm-APD laser radar. The Gm-APD laser radar for single photon detection has the advantages that the detection distance is increased, the time resolution is reduced, and when fog with the same length passes through and an object behind the fog is imaged, the effective data volume for estimating parameters of a Gamma model is reduced, so that the estimation accuracy is reduced.
Disclosure of Invention
The invention provides a single-quantity estimation-based Gm-APD laser radar fog-penetrating imaging reconstruction method, which effectively improves the recovery accuracy of targets in fog.
The invention is realized by the following technical scheme:
a Gm-APD laser radar fog penetration imaging reconstruction method based on single quantity estimation comprises the following steps:
step 1: determining the composition and distribution of imaging echoes in the foggy day, wherein the imaging echoes in the foggy day are photons received by a foggy day laser radar;
step 2: obtaining a backscattering distribution model of the Gm-APD laser radar according to the foggy day imaging echo composition and distribution in the step 1;
and step 3: measuring and calculating the attenuation coefficient mu in the backscattering distribution model obtained in the step 2 based on an attenuation coefficient calculation formula or a visibility empirical formula;
and 4, step 4: substituting the calculated attenuation coefficient mu into the backscattering distribution model in the step 2, and carrying out maximum likelihood estimation on the backscattering distribution model substituted with the attenuation coefficient mu to obtain an estimated value of the collision times k;
and 5: obtaining the backscattering photon distribution N through the estimated value of the collision times kB(bin) distribution N of backscattered photonsB(bin) and echo photon distribution N (bin) are normalized according to the maximum value, the normalization results of the two are subtracted, the result is a part which is larger than zero, a target echo signal is selected, and the target echo signal is fitted by adopting a formula (1) so as to obtain a target distance value R;
step 6: traversing all pixels to obtain a reconstructed three-dimensional range profile R after the backscattering of the fog is inhibitedxy。
Further, the photons in step 1 include: the target echo photon, the backscattering photon and the environment background photon, wherein the distribution of the target echo photon is related to the emission laser pulse waveform and the target distance, and the distribution expression of the target echo photon is as follows:
τ is the laser pulse width, NiThe number of photons after transmission attenuation, R is the target distance, c is the speed of light, and t is the propagation time of photons;
ambient background photon Nn(t) is uniformly distributed over time, expressed as:
Nn(t)＝a (2)
a is a constant.
Further, the photon propagation time in the fog is analyzed,
at the ts moment, the photon propagation distance is x, and the number of photons is N;
after one collision, at the time of ts + dt, the photon propagation distance is x + dx, and the number of photons is N-dN;
if the attenuation coefficient is μ (m)-1) The propagation velocity of a photon is v (m/s), and is expressed as
-dN＝μNdx＝μNvdt (3)
According to the formula (3), N0For the initial number of photons, the decay relationship of the photons over time is:
N＝N0exp(-μvt) (4)
according to equations (3) and (4), the photon propagation time distribution probability density p (t) is:
total propagation time
k is the number of collisions, tiThe propagation time of the photon during the collision from the i-1 th collision to the i-th collision is shown;
let utμ v, the total propagation time distribution is,
(k) is a Gamma function.
Further, the backscatter distribution model of step 2 is discrete in the time dimension and is divided by taking bins as time units, if each bin is divided into tbns, the photon propagates in the fog with a velocity equal to the speed of light, and the formula is:
μtt＝μ×3×108m/s·tb·10-9s·bin＝0.3μtb·bin (7)
then, for a Gm-APD lidar, the distribution of its back-scatter over time bin is,
further, in the step 3, when the fog concentration is controllable, the power P of the laser before passing through the fog is measured0And power P after crossingtThe method comprises the following steps:
z is the length of the mist zone.
Further, in step 3, when the attenuation coefficient cannot be directly measured, a visibility empirical formula is used for calculation, where the visibility empirical formula is:
v is visibility, lambda is laser wavelength, q is a middle variable related to visibility, and the value of q is as follows:
further, in the step 4, the calculated attenuation coefficient μ is substituted into the formula (8), and maximum likelihood estimation is performed on the formula (8) substituted into the attenuation coefficient μ, so as to obtain an estimated value of k, where the estimated value of k is expressed by:
k＝mle(data，′pdf′，NB) (12)
performing maximum likelihood estimation on the formula (8) according to the echo photon distribution N (bin) to obtain k, and further determining the formula (8), namely the backscattering photon distribution NB(bin) for the obtained NB(bin) is normalized to the original echo photon distribution N (bin) by the maximum value, and the normalized results of the two are subtracted from each other, i.e. N (bin) -NB(bin), the fraction greater than zero is denoted as N'S(bin)。
Further, in step 4, the durations of the signals/noises are sorted, the echo signal with the longest duration is selected and regarded as the target echo signal, and the echo signal is fitted by using the formula (1), and the peak position of the echo signal is used as an initial value of the fitting, so that the target distance value R is obtained.
The invention has the beneficial effects that:
the target echo peak value is lower than the backscattering noise trigger frequency, so that the backscattering distribution can be extracted, and the backscattering can be estimated more accurately when the target echo is controlled at a lower level, so that the method is more effective for foggy day data with a lower signal-to-noise ratio.
Drawings
FIG. 1 is a schematic diagram of the process of photon propagation in mist according to the present invention.
FIG. 2 is a schematic flow chart of the reconstruction method of the present invention, (a) a single-point pixel multi-frame statistical schematic diagram, (b) a schematic diagram of backward scattering photon distribution estimation, and (c) a schematic diagram of target photon distribution fitting.
FIG. 3 shows a fog penetration experiment, (a) a design experiment schematic diagram, and (b) an actual experiment diagram.
Fig. 4 shows reconstructed distance images, (a) a distance image schematic diagram of 20000 frame defogging reconstruction performed by the standard distance image method, (b) a distance image schematic diagram of 20000 frame defogging reconstruction performed by the peak value method, (c) a distance image schematic diagram of 20000 frame defogging reconstruction performed by the MIT estimation method, and (d) a distance image schematic diagram of 20000 frame defogging reconstruction performed by the single quantity estimation method of the present invention.
FIG. 5 shows the evaluation results of different frame numbers, (a) a graph of target restoration degree, and (b) a graph of relative average distance error.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1 and fig. 2, a Gm-APD lidar fog-penetrating imaging reconstruction method based on single-quantity estimation includes the following steps:
step 1: determining the composition and distribution of imaging echoes in the foggy day, wherein the imaging echoes in the foggy day are photons received by a foggy day laser radar;
step 2: obtaining a backscattering distribution model of the Gm-APD laser radar according to the foggy day imaging echo composition and distribution in the step 1;
and step 3: measuring and calculating the attenuation coefficient mu in the backscattering distribution model obtained in the step 2 based on an attenuation coefficient calculation formula or a visibility empirical formula;
and 4, step 4: and substituting the calculated attenuation coefficient mu into the backscattering distribution model in the step 2, and carrying out maximum likelihood estimation on the backscattering distribution model substituted with the attenuation coefficient mu to obtain an estimated value of the collision times k, thereby obtaining a target distance value R.
Fig. 2 (a) becomes (b) after normalization by the single quantity estimation, and (b) becomes (c) after the phase finding sorting and fitting.
As shown in fig. 2, further, the photons in step 1 include: the target echo photon, the backscattering photon and the environment background photon, wherein the distribution of the target echo photon is related to the emission laser pulse waveform and the target distance, and the distribution expression of the target echo photon is as follows:
τ is the laser pulse width, NiThe number of photons after transmission attenuation, R is the target distance, c is the speed of light, and t is the propagation time of photons;
ambient background photon Nn(t) is uniformly distributed over time, expressed as:
Nn(t)≡a (2)
a is a constant.
As shown in fig. 2, further, according to the action process of the Gm-APD lidar in the foggy day imaging as single photons and fogdrop particles, the propagation time of the photons in the fog is analyzed,
at the ts moment, the photon propagation distance is x, and the number of photons is N;
after one collision, at the time of ts + dt, the photon propagation distance is x + dx, and the number of photons is N-dN;
if the attenuation coefficient is μ (m)-1) The propagation velocity of a photon is v (m/s), and is expressed as
-dN＝μNdx＝μNvdt (3)
According to the formula (3), N0For the initial number of photons, the decay relationship of the photons over time is:
N＝N0exp(-μvt) (4)
according to equations (3) and (4), the photon propagation time distribution probability density p (t) is:
total propagation time
k is the number of collisions, tiThe propagation time of the photon from the i-1 st collision to the i-th collision is determined;
let utμ v, the total propagation time distribution is,
(k) is a Gamma function, the expression of the Gamma function is
And replacing x in the Gamma function expression by k.
Further, the step 2 is discrete in the time dimension and is divided by taking bin as a time unit if the bin is divided by the time unitEach bin is divided into tbns, then the photons travel in the fog with a velocity that approximates the speed of light, then:
μtt＝μ×3×108m/s·tb·10-9s·bin＝0.3μtb·bin (7)
then, for a Gm-APD lidar, the distribution of its back-scatter over time bin is,
further, in the step 3, when the fog concentration is controllable, the power P of the laser before passing through the fog is measured0And power P after crossingtThe method comprises the following steps:
z is the length of the mist zone.
Further, in step 3, when the attenuation coefficient cannot be directly measured, a visibility empirical formula is used for calculation, where the visibility empirical formula is:
v is visibility, lambda is laser wavelength, q is a middle variable related to visibility, and the value of q is as follows:
further, in step 4, the attenuation coefficient μ obtained by calculation is substituted into equation (8), and maximum likelihood estimation is performed on the basis of the echo data to obtain an estimated value of k, where the estimated value of k is expressed by the following equation:
k＝mle(data，′pdf′，NB) (12)
substituting the attenuation coefficient mu into equation (8) according toEcho photon distribution N (bin) carries out maximum likelihood estimation on the formula (8) to obtain k, and then the formula (8) is determined, namely, the back scattering photon distribution NB(bin) for the obtained NB(bin) is normalized to the original echo photon distribution N (bin) by the maximum value, and the normalized results of the two are subtracted from each other, i.e. N (bin) -NB(bin), the fraction greater than zero is denoted as N'S(bin)。
Further, in step 4, the duration of a certain signal or noise is defined as the number of bins occupied by the part of the certain signal or noise greater than the threshold th, and is N'sThere is a portion of the "pulse-like" noise in the (bin) that is higher in amplitude and shorter in duration, while the target duration is relatively longer;
and sequencing the duration of the signal/noise, selecting the signal with the longest duration as a target echo signal, fitting the signal by adopting a formula (1), and taking the peak position of the signal as an initial value of fitting so as to obtain a target distance value R.
Example 2
A fog penetrating platform is built indoors for imaging experiments, the experimental device is shown in figure 3, the target is a cuboid with the distance of 10m, the background is a glass wall with the distance of 12m, and the time resolution of the Gm-APD laser radar is tbThe target was imaged through a 1m long mist for 2ns, and the attenuation coefficient of the mist to the laser was measured by a 532nm laser.
The attenuation coefficient is 2.39m-1Is obtained from the formula (7)
0.3μtb＝0.3×2.39×2＝1.43(bin-1) (13)
And respectively adopting a traditional peak value method, a single quantity estimation method and an MIT estimation method to carry out target reconstruction on experimental data with different frame numbers, wherein the defogging reconstruction distance image of 20000 frames is shown in figure 4:
subjectively observing that the peak value method can not recover the actual distance image at all, wherein the distance value is concentrated in the range of 4-5 m and corresponds to the backscattering position generated by fog; the processing result obtained by adopting the MIT estimation method can be used for identifying the outline above the cuboid target according to the rarity, reducing the distance value of part of the background glass wall, and the lower half part of the distance image is still greatly influenced by the mist backscattering; compared with the prior art, the single quantity estimation method has good recovery effect on the target and the background wall, and can clearly distinguish the position contour characteristics of the target; objectively comparing the recovery effect of each method by adopting a target recovery degree and a relative average ranging error, wherein the target recovery degree is defined as:
wherein d is the recovered distance image, dsIs a standard range profile, dthFor the error tolerance, the error tolerance is set to 1 bin, i.e. 0.3m, and n is the total pixel count. The relative average range error is defined as:
the evaluation results are shown in FIG. 5:
in contrast, the target recovery degree of the single quantity estimation method is higher, and 71% of distance values can be recovered in 20000 frames, which is about 2.2 times of that of the full quantity estimation method, the recovery degree under 500 frames is 35%, even higher than 32% of that of 20000 frames in the full quantity estimation method, and the peak value method cannot reconstruct any correct distance value no matter how many frames; for the relative average distance error, the single quantity estimation method is superior at each frame number, the peak value method is almost unchanged, and although the error is smaller than the MIT estimation method at less than 6000 frames, the weak advantage is not significant because the target restoration degree is 0. In conclusion, the single-quantity estimation reconstruction algorithm has great advantages in the aspect of reconstruction of the Gm-APD laser radar fog-penetrating imaging target.
Claims (8)
1. A Gm-APD laser radar fog penetration imaging reconstruction method based on single quantity estimation is characterized by comprising the following steps:
step 1: determining the composition and distribution of imaging echoes in the foggy day, wherein the imaging echoes in the foggy day are photons received by a foggy day laser radar;
step 2: obtaining a backscattering distribution model of the Gm-APD laser radar according to the foggy day imaging echo composition and distribution in the step 1;
and step 3: measuring and calculating the attenuation coefficient mu in the backscattering distribution model obtained in the step 2 based on an attenuation coefficient calculation formula or a visibility empirical formula;
and 4, step 4: substituting the calculated attenuation coefficient mu into the backscattering distribution model in the step 2, and carrying out maximum likelihood estimation on the backscattering distribution model substituted with the attenuation coefficient mu to obtain an estimated value of the collision times k;
and 5: obtaining the backscattering photon distribution N through the estimated value of the collision times kB(bin) distribution N of backscattered photonsB(bin) and echo photon distribution N (bin) are normalized according to the maximum value, the normalization results of the two are subtracted, the result is a part which is larger than zero, a target echo signal is selected, and the target echo signal is fitted by adopting a formula (1) so as to obtain a target distance value R;
step 6: traversing all pixels to obtain a reconstructed three-dimensional range profile R after the backscattering of the fog is inhibitedxy。
2. The method for reconstructing the Gm-APD lidar fog-penetrating imaging based on single-volume estimation according to claim 1, wherein the photons in the step 1 comprise: the target echo photon, the backscattering photon and the environment background photon, wherein the distribution of the target echo photon is related to the emission laser pulse waveform and the target distance, and the distribution expression of the target echo photon is as follows:
τ is the laser pulse width, NiThe number of photons after transmission attenuation, R is the target distance, c is the speed of light, and t is the propagation time of photons;
ambient background photon Nn(t) distribution over time is uniform and constant, tableShown as follows:
Nn(t)≡a (2)
a is a constant.
3. The method for reconstructing the Gm-APD lidar fog-penetrating imaging based on single-volume estimation according to claim 2, wherein the photons are analyzed in the propagation time of the photons in the fog,
at the ts moment, the photon propagation distance is x, and the number of photons is N;
after one collision, at the time of ts + dt, the photon propagation distance is x + dx, and the number of photons is N-dN;
if the attenuation coefficient is μm-1The photon propagation speed is v m/s, expressed as,
-dN＝μNdx＝μNvdt (3)
according to the formula (3), N0For the initial number of photons, the decay relationship of the photons over time is:
N＝N0exp(-μvt) (4)
according to equations (3) and (4), the photon propagation time distribution probability density p (t) is:
total propagation time
k is the number of collisions, tiIs as follows;
let utμ v, the total propagation time distribution is,
(k) is a Gamma function.
4. The Gm-APD lidar mist-penetration formation based on single-quantity estimation according to claim 1The image reconstruction method is characterized in that the backscattering distribution model in the step 2 is discrete in a time dimension and is divided by taking bins as time units, if each bin is divided into tbns, the photon propagates in the fog with a velocity equal to the speed of light, and the formula is:
μtt＝μ×3×108m/s·tb·10-9s·bin＝0.3μtb·bin (7)
then, for a Gm-APD lidar, the distribution of its back-scatter over time bin is,
5. the method for reconstructing the Gm-APD lidar fog-penetrating imaging based on single-quantity estimation as claimed in claim 1, wherein in the step 3, when the fog concentration is controllable, the power P before the laser penetrates through the fog is measured0And power P after crossingtThe method comprises the following steps:
z is the length of the mist zone.
6. The method as claimed in claim 1, wherein in step 3, when the attenuation coefficient cannot be directly measured, the method for reconstructing the Gm-APD lidar fog-penetrating imaging based on the single quantity estimation is calculated by using a visibility empirical formula, wherein the visibility empirical formula is as follows:
v is visibility, lambda is laser wavelength, q is a middle variable related to visibility, and the value of q is as follows:
7. the method according to claim 1, wherein the step 4 is to substitute the calculated attenuation coefficient μ into equation (8), and perform maximum likelihood estimation on equation (8) substituted with attenuation coefficient μ to obtain an estimated value of k, where the estimated value of k is:
k＝mle(data，′pdf′，NB) (12)
performing maximum likelihood estimation on the formula (8) according to the echo photon distribution N (bin) to obtain k, and further determining the formula (8), namely the backscattering photon distribution NB(bin) for the obtained NB(bin) is normalized to the original echo photon distribution N (bin) by the maximum value, and the normalized results of the two are subtracted from each other, i.e. N (bin) -NB(bin), the fraction greater than zero is denoted as N'S(bin)。
8. The method for reconstructing Gm-APD lidar fog-penetrating imaging based on single-volume estimation as claimed in claim 1, wherein in step 4, the durations of the signals/noises are sorted, the longest duration is selected as the target echo signal, and the target echo signal is fitted by using formula (1), and the peak position is used as the initial value of the fitting, so as to obtain the target distance value R.
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| CN113406594B (en) * | 2021-06-01 | 2023-06-27 | 哈尔滨工业大学 | Single photon laser fog penetrating method based on double-quantity estimation method |
| CN113325436A (en) * | 2021-08-03 | 2021-08-31 | 中国科学院西安光学精密机械研究所 | Single photon imaging system simulation model based on backscattering model and modeling method |
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