A deterministic filterbank 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. Recent work by Fontaine and Peremans have shown that a sparse representation model for bat echolocation calls facilitates distinguishing objects spaced as closely as 2 micro-seconds in timedelay and was also robust to noise over a realistic range of signal to noise ratios (SNR). Fontaine and Peremans used the random FIR filter Compressive Sensing (CS) technique as their input method. Their study demonstrated that the undersampled data provided by the FIR filter output still contains sufficient information to accurately reconstruct and resolve sparse target signatures using L1 minimization techniques from CS. Their work raises the intriguing question as to whether under-sampled sensing approaches structured more like the bat's auditory system still contain the information necessary for the hyper-resolution observed in behavioral tests. This research investigates the ability to estimate sparse echo signatures using a downsampled filterbank for the sensing basis that is closer to a bat auditory system than randomized FIR filters. The returning echoes are sensed using a discrete-time constant-bandwidth filter bank followed by downsampling that loosely resembles the filtering and smoothing of the bat's cochlea. L1 minimization then reconstructs the sparse target return from this under-sampled signal. Initial simulations demonstrate that this filterbank CS model reconstructs sparse sonar targets with a high degree of accuracy while substantially undersampling the filter outputs. In addition, the overdecimated filterbank CS approach has better target resolution than the Matched Filter for SNR values ranging from 5-45 dB and has better detection performance than the Inverse Filter method. This is all accomplished while undersampling the return echo signal by as much as a factor of six. The deterministic sensing basis has the distinct advantage over the random sensing basis in the respect that the circulant structure of the filterbank sensing matrix can easily be implemented in electric circuits.