Depth Estimation Method for Single‐Photon LiDAR Under Low Signal‐to‐Noise Ratio

Liangliang Bai; Mingjun Wang; Jihua Yu; Yiming Zhou; Xin Gao

doi:10.3788/CJL241163

Chinese Journal of Lasers, Volume. 52, Issue 6, 0610003(2025)

Depth Estimation Method for Single‐Photon LiDAR Under Low Signal‐to‐Noise Ratio

Liangliang Bai^1,2, Mingjun Wang^1,3,4、*, Jihua Yu¹, Yiming Zhou¹, and Xin Gao¹

Author Affiliations

¹School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, Shaanxi , China

²School of Information Engineering, Xinjiang Institute of Engineering, Urumqi 830091, Xinjiang , China

³Xi’an Key Laboratory of Wireless Optical Communication and Network Research, Xi’an 710048, Shaanxi , China

⁴School of Physics and Telecommunications Engineering, Shaanxi University of Technology, Hanzhong 723001, Shaanxi , China

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Abstract Get PDF(in Chinese)

Figures & Tables(11)

Fig. 1. Photon-counting LiDAR depth map reconstruction algorithm

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Fig. 2. Time-domain filtering method. （a） Detection time of single pixel；（b） adjacent photon detection time difference；（c） photon counts in different time windows

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Fig. 3. Structure of BP neural network

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Fig. 4. Simulated processing results for Reindeer scenes at SNR of 0.03. (a) Absolute error map before processing by BP neural network; (b) absolute error map after processing by BP neural network

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Fig. 5. Thumbnails of the simulation dataset. (a) Art scene; (b) Bowling scene; (c) Laundry scene; (d) Reindeer scene

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Fig. 6. Dept image reconstruction results of each algorithm for the four scenes at SNR of 0.03, where True Depth denotes the ground truth of the depth map provided by the dataset. (a) Reconstructed Art scene; (b) reconstructed Bowling scene; (c) reconstructed Laundry scene; (d) reconstructed Reindeer scene

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Fig. 7. Root mean square error of photon counting LiDAR depth image reconstruction using three algorithms under different scenes. (a) Art scene; (b) Bowling scene; (c) Laundry scene; (d) Reindeer scene

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Table 0. [in Chinese]

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Table 0. [in Chinese]

Data： Feature set $({\hat{k}}_{i, j}, {\hat{α}}_{i, j})$ .
Result： Classifier Net.
1	Initialize $w_{p, q}$ ， $w_{q, r}$ ， $b_{q}$ and $b_{r}$ randomly， set error threshold $e_{t}$ and iteration $M$ .
2	while iteration ≤ Mdo
3	Calculate the output of hidden layer：
4	$y_{q} = f (\sum_{p = 1}^{3} w_{p, q} I_{p} + b_{q})$ ， $f (x) = \frac{2}{1 - e x p (- 2 x)} - 1$ ；
5	Calculate the output of output layer：
6	$θ_{r} = f (\sum_{q = 1}^{12} w_{q, r} y_{q} + b_{r})$ ， $f (x) = x$ ；
7	Adjust the weights of output and hidden layer with Levenberg–Marquardt algorithm^［22］：
8	$w_{q, r} = w_{q, r} + η_{1} Δ w_{q, r}$ ， $w_{p, q} = w_{p, q} + η_{1} Δ w_{p, q}$ ， $η_{1}$ is the learning factor；
9	Calculate the mean–square error
10	$e = \frac{{\sum_{r} ({\hat{l}}_{r} - θ_{r})}^{2}}{m a x (r)}$ ；
11	If $e_{t} \geq e$ then
12	end training；
13	end
14	end

Table 1. Parameter setting of BP neural network
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Table 1. Parameter setting of BP neural network
Parameter Value
Learning rate 0.001
Maximum number of training times 1000
Training target error 1×10^-6
Maximum validation checks 6
Minimum gradient 1×10^-10
Mu decrease ratio 0.1
Mu increase ratio 10

Table 2. Simulation parameter setting
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Table 2. Simulation parameter setting
Parameter Value
$τ_{s p}$ 5%
$d_{s p}$ 3
$z_{m a x}$ /m 15
$N_{r}$ 8
Time bin width /s 8×10^-12
Number of time bins 12500
Root mean square time of the laser pulse in time bins 33.75
T_wind 67.5

Table 3. Running time of different algorithms

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Table 3. Running time of different algorithms

Scene	Time /s
Scene	Shin	Rapp	Ours
Art （555 pixel×695 pixel）	25.266	75.170	69.387
Bowling （555 pixel×625 pixel）	22.514	73.811	68.373
Laundry （370 pixel×447 pixel）	10.767	33.265	31.574
Reindeer （370 pixel×447 pixel）	10.576	30.910	29.970

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Liangliang Bai, Mingjun Wang, Jihua Yu, Yiming Zhou, Xin Gao. Depth Estimation Method for Single‐Photon LiDAR Under Low Signal‐to‐Noise Ratio[J]. Chinese Journal of Lasers, 2025, 52(6): 0610003

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