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+# Resolution Limit of Single-Photon LiDAR
+This is the MATLAB implementation of the paper **Resolution Limit of Single-Photon LiDAR** - CVPR 2024, by Stanley H. Chan, Hashan K. Weerasooriya, Weijian Zhang, Pamela Abshire and Istvan Gyongy and Robert K. Henderson.
+
+
+Click on the corresponding link to
+- [**Read the Paper and Supplementary Material**](https://arxiv.org/abs/2403.17719)
+- [**Download the Data**](https://arxiv.org/abs/2403.17719)
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+
+
+## Requirements ##
+- [x] This code has been tested on MATLAB 2023a
+
+
+## Usage ##
+
+### MATLAB Scripts ###
+- Figure02_matched_filter.m *Visualize the matched filter output*.
+- Figure03_space_time.m *Visualize the effective return pulse due to obervating $\lambda(x,t)$ through $N$ pixels and pulse broadening due to slanting surfaces*.
+- Figure05_1D_mse.m *Display the simulated and MSE calculation theroretical MSE calculation for the 1D case*.
+- Figure06_1D_variance.m *Highlight the significance of the spatial term $c^2 \sigma_x^2$
+in variance calculation*.
+- Figure07_2D_mse.m *Display the simulated and MSE calculation theroretical MSE calculation for the 2D case*.
+- Figure08_******.m *Visualize the variation of the ML estimation for different spatial resolution and calculated and theoreteical MSE variation for the real 2D data*.
+- Figure11_tau.m *Display the ground truth time of arrival function for the 1D case*.
+- Figure12/13_bias_example.m *Show the limitations of the approximations for the bias term under different ground truth time of arrival function variations-smooth, stepwise, noisy*.
+- Figure14_bias_update.m *Show how the updated theoretical estimate of the bias varies with noisy ground truth*.
+- Figure16_sampling.m *Demonstrate how to use the inverse CDF to generate time stamps under different pulse shapes*.
+- Figure17_18_sampling.m *Visualize the likelihood functions original likelihood and derivative of the original likelihood for any arbitrary pulse including Gaussian*.
+- Figure19_noise_floor.m *Demonstrate that the MSE thoretical bound still holds for non zero noise floor instances*.
+- Figure20_pile_up_1D.m *Show the variation of time stamp histogram under pile-up effect*.
+- Figure21_pile_up_MSE.m *Display the MSE comparison in the presence of pile-up effect*.
+- Figure22_2D_bias.m *Demonstrate how the bias term varies in the 2D case*.
+- Figure23_2D_bias.m *Demonstrate how the variance term changes in the 2D case*.
+- real_check_alpha0.m *Calculate the total pulse energy $\alpha_0$ for the static fan real dataset*.
+- real_check_sigma_t.m *Calculate the pulse variance $\sigma_t$ for the static fan real dataset*.
+- real_preprocess.m *Preprocess the timestamp data for the static fan real dataset*.
+
+
+
+### MATLAB functions ###
+
+- generate_time_stamps.m *Generate $M$ random timestamps following the provided pulse function $\lambda(t)$*.
+- myLikelihood.m *Calculate negative log likelihood values for given set of time stamps when the pulse is Gaussian*.
+- myLikelihood_dt.m *Calculate the derivative of the negative log likelihood at given set of time stamps when the pulse is Gaussian*.
+- myLikelihood_general.m *Calculate the derivative of the negative log likelihood values for given set of time stamps for any given arbitrary pulse*.
+- myLikelihood_general_dt.m *Calculate the derivative of the negative log likelihood at given set of time stamps and for any given arbitrary pulse*.
+
+
+
+
+## arXiv Citation ##
+If you find this paper to be valuable for your research, kindly consider citing our work.
+```
+@misc{chan2024resolution,
+ title={Resolution Limit of Single-Photon LiDAR},
+ author={Stanley H. Chan and Hashan K. Weerasooriya and Weijian Zhang and Pamela Abshire and Istvan Gyongy and Robert K. Henderson},
+ year={2024},
+ eprint={2403.17719},
+ archivePrefix={arXiv},
+ primaryClass={eess.SP}
+}
+```
+
+## Contact Information ##
+Please email *hweeraso@purdue.edu* if you have any difficulty replicating the results.
+