  This research addresses the challenge of estimating bathymetry from imaging
sonars where the state-of-the-art works have primarily relied on either
supervised learning with ground-truth labels or surface rendering based on the
Lambertian assumption. In this letter, we propose a novel, self-supervised
framework based on volume rendering for reconstructing bathymetry using
forward-looking sonar (FLS) data collected during standard surveys. We
represent the seafloor as a neural heightmap encapsulated with a parametric
multi-resolution hash encoding scheme and model the sonar measurements with a
differentiable renderer using sonar volumetric rendering employed with
hierarchical sampling techniques. Additionally, we model the horizontal and
vertical beam patterns and estimate them jointly with the bathymetry. We
evaluate the proposed method quantitatively on simulation and field data
collected by remotely operated vehicles (ROVs) during low-altitude surveys.
Results show that the proposed method outperforms the current state-of-the-art
approaches that use imaging sonars for seabed mapping. We also demonstrate that
the proposed approach can potentially be used to increase the resolution of a
low-resolution prior map with FLS data from low-altitude surveys.
