Gaussian Process Convolutional Dictionary Learning

Convolutional dictionary learning (CDL), the problem of estimating shift-invariant templates from data, is typically conducted in absence a prior/structure on templates. In data-scarce or low signal-to-noise ratio (SNR) regimes, learned overfit data and lack smoothness, which can affect predictive performance downstream tasks. To address this limitation, we propose GPCDL, convolutional framework that enforces priors using Gaussian Processes (GPs). With focus show theoretically imposing GP prior equivalent to Wiener filtering templates, thereby suppressing high-frequency components promoting smoothness. We algorithm simple extension classical iteratively reweighted least squares algorithm, independent choice kernels. This property allows one experiment flexibly with different smoothness assumptions. Through simulation, GPCDL learns smooth dictionaries better accuracy than unregularized alternative across range SNRs. an application neural spiking more accurate visually-interpretable dictionary, leading superior compared non-regularized CDL, as well parametric alternatives.