  Imaging methods based on array signal processing often require a fixed
propagation speed of the medium, or speed of sound (SoS) for methods based on
acoustic signals. The resolution of the images formed using these methods is
strongly affected by the assumed SoS, which, due to multipath, nonlinear
propagation, and non-uniform mediums, is challenging at best to select. In this
letter, we propose a Bayesian approach to marginalize the influence of the SoS
on beamformers for imaging. We adapt Bayesian direction-of-arrival estimation
to an imaging setting and integrate a popular minimum variance beamformer over
the posterior of the SoS. To solve the Bayesian integral efficiently, we use
numerical Gauss quadrature. We apply our beamforming approach to shallow water
sonar imaging where multipath and nonlinear propagation is abundant. We compare
against the minimum variance distortionless response (MVDR) beamformer and
demonstrate that its Bayesian counterpart achieves improved range and azimuthal
resolution while effectively suppressing multipath artifacts.
