A fast transform for acoustic imaging with separable arrays

Acoustic imaging is a computationally intensive and ill-conditioned inverse problem, which involves estimating high resolution source distributions with large microphone arrays. In this paper we show how to significantly decrease its computational cost with a fast transform designed for separable array geometries. This transform provides a natural and elegant way of accelerating beamforming, deconvolution methods and regularized least-squares solvers. We accelerate image deconvolution by 10x with respect to FFT-based methods, and accelerate other important imaging algorithms (based on explicit matrix multiplication) by even larger factors. Because of these gains in computational speed, one can reconstruct images with higher resolutions than previously possible, and also enable more accurate reconstruction techniques, opening new and exciting possibilities for acoustic imaging.