# Using Frame Theoretic Convolutional Gridding for Robust Synthetic Aperture Sonar Imaging

## TL;DR

This paper introduces a novel frame theoretic convolutional gridding method to improve the robustness and accuracy of synthetic aperture sonar imaging, addressing limitations of traditional Fourier domain approaches.

## Contribution

It proposes the FTCG algorithm, extending NUFFT techniques to enhance SAS image reconstruction accuracy with minimal additional computational cost.

## Key findings

- FTCG improves reconstruction accuracy over traditional methods.
- Simulation results demonstrate enhanced robustness to speckle and sound-speed errors.
- Method maintains computational efficiency comparable to existing approaches.

## Abstract

Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in both accuracy and efficiency. There are, however, inherent limitations to current SAS reconstruction methodology. In particular, popular and efficient Fourier domain SAS methods require a 2D interpolation which is often ill conditioned and inaccurate, inevitably reducing robustness with regard to speckle and inaccurate sound-speed estimation. To overcome these issues, we propose using the frame theoretic convolution gridding (FTCG) algorithm to handle the non-uniform Fourier data. FTCG extends upon non-uniform fast Fourier transform (NUFFT) algorithms by casting the NUFFT as an approximation problem given Fourier frame data. The FTCG has been show to yield improved accuracy at little more computational cost. Using simulated data, we outline how the FTCG can be used to enhance current SAS processing.