{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:33:31Z","timestamp":1760146411198,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T00:00:00Z","timestamp":1730332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shenzhen Science and Technology Program","award":["KQTD20190929172704911","202201011709"],"award-info":[{"award-number":["KQTD20190929172704911","202201011709"]}]},{"name":"Guangzhou Science and Technology Plan Project","award":["KQTD20190929172704911","202201011709"],"award-info":[{"award-number":["KQTD20190929172704911","202201011709"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the case of a weak signal from a photon counting lidar and strong noise from the solar background, the signal is completely submerged by noise, potentially resulting in the appearance of multiple peaks in the denoising algorithm of photon counting entropy. Consequently, a clear distinction between the signal and noise may become challenging, leading to significant fluctuation in the ranging error. To solve this problem, this paper proposes an improved offset parameter optimization algorithm under the framework of photon counting entropy, aiming to effectively eliminate peak interference caused by noise and enhancing ranging accuracy. The algorithm includes two aspects. First, we introduce the solar irradiance prediction of an MLP network and least squares linear conversion to accurately estimate the noise rate of the solar background noise. Then, we propose the offset parameter optimization method to effectively mitigate the interference caused by noise. In simulation and experimental analyses, the ranging error of our proposed method is within 5 and 30 cm, respectively. Compared with the denoising method of photon counting entropy, the average ranging error is increased by 81.99% and 73.76%. Furthermore, compared to other anti-noise methods, it exhibits superior ranging capability.<\/jats:p>","DOI":"10.3390\/e26110934","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T13:09:27Z","timestamp":1730466567000},"page":"934","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Offset Parameter Optimization Algorithm for Denoising in Photon Counting Lidar"],"prefix":"10.3390","volume":"26","author":[{"given":"Zhuangbin","family":"Tan","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9890-8380","authenticated-orcid":false,"given":"Yan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronics and Communication Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0630-602X","authenticated-orcid":false,"given":"Ziwen","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5840-0021","authenticated-orcid":false,"given":"Jintao","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanjie","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0493-6263","authenticated-orcid":false,"given":"Feifan","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheyu","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renli","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongxing","family":"Jiao","sequence":"additional","affiliation":[{"name":"School of Electronics and Communication Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Huang, M., Zhang, Z., Xie, J., Li, J., and Zhao, Y. (2021). An entropy-based anti-noise method for reducing ranging error in photon counting lidar. Entropy, 23.","DOI":"10.3390\/e23111499"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.measurement.2003.11.003","article-title":"Signal induced noise in PMT detection of lidar signals","volume":"35","author":"Acharya","year":"2004","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.measurement.2004.11.014","article-title":"Lidar determination of altitude profile of the refraction index in electro-optical monitoring of the Earth\u2019s atmosphere","volume":"37","author":"Prezhdo","year":"2005","journal-title":"Measurement"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"108405","DOI":"10.1016\/j.measurement.2020.108405","article-title":"An EEMD-SVD-LWT algorithm for denoising a lidar signal","volume":"168","author":"Cheng","year":"2021","journal-title":"Measurement"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kovale, V.A., and Eichinger, W.E. (2004). Elastic Lidar Theory, Practice, and Analysis Methods, Wiley-Interscience.","DOI":"10.1002\/0471643173"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Bohren, C.F., and Huffman, D.R. (1998). Absorption and Scattering of Light by Small Particles, John Wiley & Sons.","DOI":"10.1002\/9783527618156"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1016\/j.jqsrt.2009.02.035","article-title":"Aerosol light absorption and its measurement: A review","volume":"110","author":"Moosmuller","year":"2009","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.measurement.2016.10.009","article-title":"Quantifying the influence of rain in LiDAR performance","volume":"95","author":"Filgueira","year":"2017","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"A936","DOI":"10.1364\/OE.27.00A936","article-title":"Impact of solar background radiation on the accuracy of wind observations of spaceborne doppler wind lidars based on their orbits and optical parameters","volume":"27","author":"Zhang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"30199","DOI":"10.1364\/OE.404681","article-title":"Adaptive single photon detection under fluctuating background noise","volume":"28","author":"Chen","year":"2020","journal-title":"Opt. Express"},{"key":"ref_11","unstructured":"Konnik, M., and Welsh, J. (2014). High-level numerical simulations of noise in CCD and CMOS photosensors: Review and tutorial. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5744","DOI":"10.1109\/TSP.2010.2057427","article-title":"An optimal basis of band-limited functions for signal analysis and design","volume":"58","author":"Wei","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1002\/nav.3800030109","article-title":"An algorithm for quadratic programming","volume":"3","author":"Frank","year":"1956","journal-title":"Nav. Res. Logist. Q."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1109\/TSP.2022.3177845","article-title":"Memory-efficient convex optimization for self-dictionary separable nonnegative matrix factorization: A Frank-Wolfe approach","volume":"70","author":"Nguyen","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1007\/s11075-018-0565-4","article-title":"Convergence rates of accelerated prodimal gradient algorithms under independent noise","volume":"81","author":"Sun","year":"2019","journal-title":"Numer. Algorithms"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1505809","DOI":"10.1109\/JPHOT.2019.2951111","article-title":"A method for maintaining the stability of range walk error in photon counting lidar with probability distribution regulator","volume":"11","author":"Xie","year":"2019","journal-title":"IEEE Photonics J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"67997","DOI":"10.1007\/s11042-024-18197-w","article-title":"Image denoising method based on improved wavelet threshold algorithm","volume":"83","author":"Zhu","year":"2024","journal-title":"Multimed. Tools Appl."},{"key":"ref_18","first-page":"5005","article-title":"Underwater depth imaging using time-correlated single-photon counting","volume":"21","author":"Maccarone","year":"2015","journal-title":"Opt. Express"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"896708","DOI":"10.1155\/2010\/896708","article-title":"Full waveform analysis for long-range 3D imaging laser radar","volume":"2010","author":"Wallace","year":"2010","journal-title":"Eurasip J. Adv. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Huang, M., Zhang, Z., Cen, L., Li, J., Xie, J., and Zhao, Y. (2023). Prediction of the number of cumulative pulses based on the photon statistical entropy evaluation in photon counting lidar. Entropy, 25.","DOI":"10.3390\/e25030522"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"112464","DOI":"10.1016\/j.rse.2021.112464","article-title":"Determining maximum entropy in 3D remote sensing height distributions and using it to improve aboveground biomass modelling via stratification","volume":"260","author":"Adnan","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5705018","DOI":"10.1109\/TGRS.2023.3323963","article-title":"A Maximum Entropy-Based Optimal Neighbor Selection for Multispectral Airborne LiDAR Point Cloud Classification","volume":"61","author":"Jiang","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4100313","DOI":"10.1109\/TGRS.2021.3051799","article-title":"Satellite-Derived Aerosol Optical Depth Fusion Combining Active and Passive Remote Sensing Based on Bayesian Maximum Entropy","volume":"60","author":"Xia","year":"2022","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.rse.2014.11.001","article-title":"Urban land cover classification using airborne lidar data: A review","volume":"158","author":"Yan","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1117\/12.486384","article-title":"Analysis of Geiger-mode APD laser radars","volume":"Volume 5086","author":"Kamerman","year":"2003","journal-title":"Laser Radar Technology and Applications VIII"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8838","DOI":"10.1364\/AO.433461","article-title":"Theoretical model considering optimal ranging performance and energy efficiency for photon-counting lidars with multiple detectors","volume":"60","author":"Yang","year":"2021","journal-title":"Appl. Opt."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"15924","DOI":"10.1364\/OE.26.015924","article-title":"Theoretical ranging performance model and range walk error correction for photon counting lidars with multiple detectors","volume":"26","author":"Ma","year":"2018","journal-title":"Opt. Express"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.jqsrt.2017.06.038","article-title":"The HITRAN2016 molecular spectroscopic database","volume":"203","author":"Gordon","year":"2017","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_29","first-page":"107","article-title":"On the light from the sky, its polarization and color","volume":"41","author":"Rayleigh","year":"1970","journal-title":"Philos. Mag."},{"key":"ref_30","first-page":"447","article-title":"On the scattering of light by small particles","volume":"41","author":"Rayleigh","year":"1958","journal-title":"Philos. Mag."},{"key":"ref_31","unstructured":"Mcccarney, E.J. (1977). Optics of Atmosphere: Scattering by Molecules and Particles, John Wiley & Sons."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Jadidi, A., Menezes, R., De Souza, N., and de Castro Lima, A.C. (2018). A hybrid GA\u2013MLPNN model for one-hour-ahead forecasting of the global horizontal irradiance in Elizabeth city, North Carolina. Energies, 11.","DOI":"10.3390\/en11102641"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"102057","DOI":"10.1016\/j.asej.2022.102057","article-title":"Deep learning model for regional solar radiation estimation using satellite images","volume":"14","author":"Yuzer","year":"2023","journal-title":"Ain Shams Eng. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"125637","DOI":"10.1016\/j.energy.2022.125637","article-title":"Battery state-of-health estimation based on multiple charge and discharge features","volume":"263","author":"Agudelo","year":"2023","journal-title":"Energy"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.energy.2018.09.108","article-title":"The determinants of residential energy expenditure in Italy","volume":"165","author":"Besagni","year":"2018","journal-title":"Energy"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103165","DOI":"10.1016\/j.seta.2023.103165","article-title":"Arithmetic optimization with hybrid deep learning algorithm based solar radiation prediction model","volume":"57","author":"Irshad","year":"2023","journal-title":"Sustain. Energy Technol. Assessments"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.apenergy.2017.10.076","article-title":"An efficient neuro-evolutionary hybrid modeling mechanism for the estimation of daily global solar radiation in the Sunshine State of Australia","volume":"209","author":"Deo","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"111759","DOI":"10.1016\/j.measurement.2022.111759","article-title":"Deep learning CNN-LSTM-MLP hybrid fusion model for feature optimizations and daily solar radiation prediction","volume":"202","author":"Ghimire","year":"2022","journal-title":"Measurement"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.enconman.2017.11.067","article-title":"Short-term wind speed forecasting based on fast ensemble empirical mode decomposition, phase space reconstruction, sample entropy and improved back-propagation neural network","volume":"157","author":"Sun","year":"2018","journal-title":"Energy Convers. Manag."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1016\/j.renene.2021.06.129","article-title":"Estimating half-hourly solar radiation over the Continental United States using GOES-16 data with iterative random forest","volume":"178","author":"Chen","year":"2021","journal-title":"Renew. Energy"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.apenergy.2013.02.053","article-title":"Estimating the daily global solar radiation spatial distribution from diurnal temperature ranges over the Tibetan Plateau in China","volume":"107","author":"Pan","year":"2013","journal-title":"Appl. Energy"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/11\/934\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:25:25Z","timestamp":1760113525000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/11\/934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,31]]},"references-count":41,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["e26110934"],"URL":"https:\/\/doi.org\/10.3390\/e26110934","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,10,31]]}}}