Uwe Friederich, Stephen A. Billings, Mikko A. Juusola, Daniel Coca
Sensory Adaptation, NARMAX, Nonlinear SystemIdentification, Wavelet Multiresolution Approximation,Photoreceptor
Adaptation is a fundamental characteristic of sensory processing. It enables sensory neurones to map efficiently the extensive range of environmental signals onto their limited dynamic range in order to prevent saturation and to maximize the amount of information collected. This paper presents a novel two-step approach for identifying both the nonlinear dynamical model and the time evolution of the gain of a self-adaptive sensory system based on experimental data. The first step involves estimating a set of fixed-parameter models which are used to determine the underlying stimulus-invariant model structure and the set of parameters that change during adaptation. Subsequently, the inverse problem of estimating the time evolution of these parameters during adaptation can be formulated as an infinite-dimensional nonlinear constrained optimisation problem where the constraint is represented by the ‘forward’ time-invariant dynamical model derived in the first step. The gain function is estimated by solving an approximate finite- dimensional optimization problem derived using orthogonal Battle‐Lemarie scaling basis functions. The applicability of the proposed approach is demonstrated through numerical simulation and using experimental data consisting of intracellular voltage responses recorded from fly photoreceptors subjected to light patterns over a wide range of luminance levels.
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