# SH-SAS: An Implicit Neural Representation for Complex Spherical-Harmonic Scattering Fields for 3D Synthetic Aperture Sonar

arXiv: https://arxiv.org/abs/2509.11087 · HTML: https://mlsanity.com/paper/2509.11087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [T"oRF: Time-of-Flight Radiance Fields for Dynamic Scene View Synthesis](https://mlsanity.com/paper/2109.15271/) (2021)
- [Non-line-of-Sight Imaging via Neural Transient Fields](https://mlsanity.com/paper/2101.00373/) (2021)
- [Neural Implicit Surface Reconstruction using Imaging Sonar](https://mlsanity.com/paper/2209.08221/) (2022)
- [DART: Implicit Doppler Tomography for Radar Novel View Synthesis](https://mlsanity.com/paper/2403.03896/) (2024)
- [Transient Neural Radiance Fields for Lidar View Synthesis and 3D Reconstruction](https://mlsanity.com/paper/2307.09555/) (2023)
- [Radar Fields: Frequency-Space Neural Scene Representations for FMCW Radar](https://mlsanity.com/paper/2405.04662/) (2024)
- [Neural Volumetric Reconstruction for Coherent Synthetic Aperture Sonar](https://mlsanity.com/paper/2306.09909/) (2023)
- [Neural Implicit Surface Reconstruction of Freehand 3D Ultrasound Volume with Geometric Constraints](https://mlsanity.com/paper/2401.05915/) (2024)
- [AONeuS: A Neural Rendering Framework for Acoustic-Optical Sensor Fusion](https://mlsanity.com/paper/2402.03309/) (2024)
- [Bathymetric Surveying with Imaging Sonar Using Neural Volume Rendering](https://mlsanity.com/paper/2404.14819/) (2024)
- [Transientangelo: Few-Viewpoint Surface Reconstruction Using Single-Photon Lidar](https://mlsanity.com/paper/2408.12191/) (2024)
- [SpINR: Neural Volumetric Reconstruction for FMCW Radars](https://mlsanity.com/paper/2503.23313/) (2025)
- [GPU Acceleration for Synthetic Aperture Sonar Image Reconstruction](https://mlsanity.com/paper/2101.05888/) (2021)
- [SINR: Deconvolving Circular SAS Images Using Implicit Neural Representations](https://mlsanity.com/paper/2204.10428/) (2022)
- [Multi-view 3D surface reconstruction from SAR images by inverse rendering](https://mlsanity.com/paper/2502.10492/) (2025)
- [Approximate Extraction of Late-Time Returns via Morphological Component Analysis](https://mlsanity.com/paper/2208.06056/) (2022)
- [NeRF-enabled Analysis-Through-Synthesis for ISAR Imaging of Small Everyday Objects with Sparse and Noisy UWB Radar Data](https://mlsanity.com/paper/2410.10085/) (2024)

## Built on by (most cited first, 1 of 1)

- [Neural Radiated-Noise Fields for Unmanned Underwater Vehicle Noise Spectrum Prediction in Three-Dimensional Scenes](https://mlsanity.com/paper/2606.04008/) (2026)

## Abstract (arXiv)

Synthetic aperture sonar (SAS) reconstruction requires recovering both the spatial distribution of acoustic scatterers and their direction-dependent response. Time-domain backprojection is the most common 3D SAS reconstruction algorithm, but it does not model directionality and can suffer from sampling limitations, aliasing, and occlusion. Prior neural volumetric methods applied to synthetic aperture sonar treat each voxel as an isotropic scattering density, not modeling anisotropic returns. We introduce SH-SAS, an implicit neural representation that expresses the complex acoustic scattering field as a set of spherical harmonic (SH) coefficients. A multi-resolution hash encoder feeds a lightweight MLP that outputs complex SH coefficients up to a specified degree L. The zeroth-order coefficient acts as an isotropic scattering field, which also serves as the density term, while higher orders compactly capture directional scattering with minimal parameter overhead. Because the model predicts the complex amplitude for any transmit-receive baseline, training is performed directly from 1-D time-of-flight signals without the need to beamform intermediate images for supervision. Across synthetic and real SAS (both in-air and underwater) benchmarks, results show that SH-SAS performs better in terms of 3D reconstruction quality and geometric metrics than previous methods.