Splitted Wavelet Differential Inclusion for neural signal processing
Keywords: Wavelet smoothing, differential inclusion, weak signal, signal reconstruction, Parkinson's disease, burst activity
TL;DR: We propose a new Wavelet smoothing method to enhance the signal reconstruction in neuroscience applications.
Abstract: Wavelet shrinkage is a powerful tool in neural signal processing. It has been applied to various types of neural signals, such as non-invasive signals and extracellular recordings. For example, in Parkinson's disease (PD), $\beta$ burst activities in local field potentials (LFP) signals indicated pathological information, which corresponds to \emph{strong signal} with higher wavelet coefficients. However, it has been found that there also exists \emph{weak signal} that should not be ignored. This weak signal refers to the set of small coefficients, which corresponds to the non-burst/tonic activity in PD. While it lacks the interpretability of the strong signal, neglecting it may result in the omission of movement-related information during signal reconstruction. However, most existing methods mainly focused on strong signals, while ignoring weak signals. In this paper, we propose \emph{Splitted Wavelet Differential Inclusion}, which is provable to achieve better estimation of both the strong signal and the whole signal. Equipped with an $\ell_2$ splitting mechanism, we derive the solution path of a couple of parameters in a newly proposed differential inclusion, of which the sparse one can remove bias in estimating the strong signal and the dense parameter can additionally capture the weak signal with the $\ell_2$ shrinkage. The utility of our method is demonstrated by the improved accuracy in a numerical experiment and additional findings of tonic activity in PD.
Primary Area: applications to neuroscience & cognitive science
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Submission Number: 12724
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