  Synthetic aperture sonar (SAS) measures a scene from multiple views in order
to increase the resolution of reconstructed imagery. Image reconstruction
methods for SAS coherently combine measurements to focus acoustic energy onto
the scene. However, image formation is typically under-constrained due to a
limited number of measurements and bandlimited hardware, which limits the
capabilities of existing reconstruction methods. To help meet these challenges,
we design an analysis-by-synthesis optimization that leverages recent advances
in neural rendering to perform coherent SAS imaging. Our optimization enables
us to incorporate physics-based constraints and scene priors into the image
formation process. We validate our method on simulation and experimental
results captured in both air and water. We demonstrate both quantitatively and
qualitatively that our method typically produces superior reconstructions than
existing approaches. We share code and data for reproducibility.
