Computationally efficient regularized acoustic imaging

Sparse recovery techniques have been shown to produce very accurate acoustic images, significantly outperforming traditional deconvolution approaches. However, so far these proposals have been computationally intractable for all but very small images, because they had no means of efficiently transforming back and forth between a hypothetical image under reconstruction and the measured data. In this paper we obtain a fast transform for planar array geometries using the fast non-equispaced Fourier transform (NFFT). We then apply it to accelerate general-purpose solvers by several orders of magnitude, enabling computationally-efficient regularized acoustic imaging. The proposed approach is not only tractable, but faster than competing deconvolution techniques, while delivering reconstructions with unprecedented accuracy.