A deterministic compressive sensing model for bat biosonar.

The big brown bat (Eptesicus fuscus) uses frequency modulated (FM) echolocation calls to accurately estimate range and resolve closely spaced objects in clutter and noise. They resolve glints spaced down to 2 μs in time delay which surpasses what traditional signal processing techniques can achieve using the same echolocation call. The Matched Filter (MF) attains 10-12 μs resolution while the Inverse Filter (IF) achieves higher resolution at the cost of significantly degraded detection performance. Recent work by Fontaine and Peremans [J. Acoustic. Soc. Am. 125, 3052-3059 (2009)] demonstrated that a sparse representation of bat echolocation calls coupled with a decimating sensing method facilitates distinguishing closely spaced objects over realistic SNRs. Their work raises the intriguing question of whether sensing approaches structured more like a mammalian auditory system contains the necessary information for the hyper-resolution observed in behavioral tests. This research estimates sparse echo signatures using a gammatone filterbank decimation sensing method which loosely models the processing of the bat's auditory system. The decimated filterbank outputs are processed with [script-l](1) minimization. Simulations demonstrate that this model maintains higher resolution than the MF and significantly better detection performance than the IF for SNRs of 5-45 dB while undersampling the return signal by a factor of six.