Fast near-field 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. We have recently shown how to significantly accelerate acoustic imaging under a far-field approximation using fast transforms. This paper generalizes our previous work to obtain computationally efficient and accurate transforms for near-field imaging with separable arrays. We show that under a suitable permutation, the imaging transform can be made nearly separable, even when modeling strong near-field effects. We exploit this quasi-separability to obtain a computationally efficient and accurate low-rank representation, allowing the design of fast transforms for near-field operation with arbitrary focal surfaces and arbitrary accuracy. We combine these transforms with calibration matrices, which compensate non-separable characteristics and allow one to quickly reshape focal surfaces without having to recompute the optimal transforms.