Super-resolution acoustic imaging using non-uniform spatial dictionaries

Super-resolution acoustic imaging is a powerful technique for sound field analysis in which a mixture of acoustic signals is decomposed into a sparse set of components selected from a dictionary of spatial directions. In previous work, we have shown that sparse recovery with a reasonably uniform spatial dictionary can be used to increase the resolution of the image of the sound field recorded by a spherical microphone array. In this work, we explore the impact of using a non-uniform spatial dictionary on the resulting acoustic image. More precisely, we explore refining or increasing the resolution of the spatial dictionary in the region of interest, while coarsening or decreasing the spatial resolution of the dictionary for the rest of space. The motivations for modifying the sparse-recovery spatial dictionary are: (1) to enable one to zoom in to a particular region of space; (2) to allow a subdivision of the acoustic imaging problem, whereby different regions of space are successively examined; and (3) to enable one to reduce the overall size of the spatial dictionary and thus reduce the computational requirements of the sparse recovery algorithm. In this paper, we explore the robustness of super-resolution acoustic imaging to non-uniform spatial dictionaries. Simulations indicate that accurate acoustic images can still be obtained with non-uniform spatial dictionaries.