Super-resolution time-frequency decomposition with hyperlets for neural spike analysis

• The hyperlet improves the perceived time-frequency resolution • The hyperlet dramatically speeds up super-resolution operations • Hyperlet-based preprocessing improves clustering of fast, complex neuronal spikes • The hyperlet is applicable to improve pattern recognition across various domains Time-frequency decomposition is a well-established method to unmix signals generated by multiple sources with unique characteristics. However, there are cases of high signal complexity where existing time-frequency decomposition tools are insufficient for localizing and representing short-bursting signals. One example is the currently highly popular extracellular low-impedance recordings from multi-electrode arrays in the brain in vivo where each neuron repeatedly generates a specific signal ’fingerprint’ (characteristic spike waveform) that can be mixed with the signals of hundreds of other sources, including the spikes of nearby neurons. Here we derive the hyperlet, which combines multiple decompositions into one. The hyperlet transform (HLT) method in turn enables highly localized representations of short bursts compared to other super-resolution spectral estimators, while requiring orders of magnitude fewer operations. We demonstrate a substantial advantage of HLT across a variety of generic, complex signals and signal burst unmixing tasks. We proceed by showing that HLT greatly facilitates for a generic classifier to separate specific neuronal spikes with high fidelity in challenging and complex recording signals from the neocortex in vivo , compared to when the classifier operates directly on the voltage signal of the spikes. We also exemplify HLT’s generic signal processing capability by achieving high resolution decomposition of complex acoustic data.