Efficient estimation of phase response curves via compressive sensing
© Hong and De Schutter; licensee BioMed Central Ltd. 2011
Published: 18 July 2011
The phase-response curve (PRC), relating the phase shift of the oscillator and externally given perturbation , is one of the most important tools for characterizing the biological oscillators, such as neurons, and studying their synchronization in a network . In experiments, the PRC can be estimated by measuring the phase changes with given stimuli, and several methods have been proposed (reviewed in ). One of the problems in such estimation is that the timescales of a PRC, naturally inherited from neuronal dynamics, are around the range of interspike intervals, while the external stimuli, such as pulses or continuous noise, usually have strong power in higher frequency ranges. This problem has been addressed in many ways such as simple averaging , randomly selecting low frequency Fourier modes [2, 3], assuming smooth priors , etc.
Here we propose a systematic and efficient approach of estimating the PRC based on the recently developed method in signal processing called Compressive Sensing (CS) . CS is a framework for estimation of sparsely constructed signals from random observations, and therefore suitable for discovering a small number of low frequency Fourier modes composing the PRC from the experimental measurements with a much wider frequency spectrum.
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