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Physically Motivated Distributions for Bayesian Deep Learning of Synthetic Aperture Sonar Imaging Artifacts
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DOI：10.1109/lgrs.2026.3715375.png)
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Abstract
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We demonstrate that the choice of weight prior in Bayesian neural networks (BNNs) is a consequential and nontrivial design decision for synthetic aperture sonar (SAS) imaging artifact classification. Motivated by established statistical models of acoustic seafloor backscatter, we replace the standard univariate Gaussian prior on the first convolutional layer with physically motivated alternatives: a multivariate normal (MVN) prior that captures empirical pixel covariance, and asymmetric priors comprising the Gumbel model, which corresponds to a log-transformed Weibull distribution. All priors are implemented via local reparameterization with closed-form Kullback–Leibler (KL) divergence, preserving computational tractability. On a dataset of 54 geographically diverse SAS images comprising <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3 \times 10^{5} ~300 \times 300$ </tex-math></inline-formula> pixel patches, the Gumbel prior yields 97.6% macro <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F1$ </tex-math></inline-formula> and 0.7% expected calibration error (ECE) on ResNet20, versus 87.1% <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F1$ </tex-math></inline-formula> and 9.7% ECE for the Gaussian baseline. On ResNet50, Gumbel achieves 99.2% accuracy, surpassing the deterministic model. Therefore, prior specification deserves domain-specific consideration in BNN deployments.
Keywords:
Bayesian deep learning
Bayesian neural network (BNN)
image statistics
synthetic aperture sonar (SAS)
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