# Bayesian 3D Reconstruction of Subsampled Multispectral Single-photon Lidar Signals

## TL;DR

This paper introduces a Bayesian 3D reconstruction method for multispectral single-photon Lidar that efficiently reconstructs multiple surfaces with fewer photons and measurements, reducing acquisition time and computational load.

## Contribution

The novel Bayesian algorithm jointly processes spectral bands and models spatial correlations, enabling accurate multi-surface reconstruction from subsampled data with less photon detection.

## Key findings

- Better reconstruction accuracy than existing methods.
- Effective subsampling schemes reduce measurements without performance loss.
- Demonstrated on synthetic and real data.

## Abstract

Light detection and ranging (Lidar) single-photon devices capture range and intensity information from a 3D scene. This modality enables long range 3D reconstruction with high range precision and low laser power. A multispectral single-photon Lidar system provides additional spectral diversity, allowing the discrimination of different materials. However, the main drawback of such systems can be the long acquisition time needed to collect enough photons in each spectral band. In this work, we tackle this problem in two ways: first, we propose a Bayesian 3D reconstruction algorithm that is able to find multiple surfaces per pixel, using few photons, i.e., shorter acquisitions. In contrast to previous algorithms, the novel method processes the jointly all the spectral bands, obtaining better reconstructions using less photon detections. The proposed model promotes spatial correlation between neighbouring points within a given surface using spatial point processes. Secondly, we account for different spatial and spectral subsampling schemes, which reduce the total number of measurements, without significant degradation of the reconstruction performance. In this way, the total acquisition time, memory requirements and computational time can be significantly reduced. The experiments performed using both synthetic and real single-photon Lidar data demonstrate the advantages of tailored sampling schemes over random alternatives. Furthermore, the proposed algorithm yields better estimates than other existing methods for multi-surface reconstruction using multispectral Lidar data.