Superresolution from Principal Component Models by RKHS Sampling
Principal component analysis (PCA) involves a signal that is sampled at some arbitrary but fixed and finite set of locations. Radial Basis Function (RBF) regression interpolates a-priori known data to arbitrary locations as a weighted sum of a (radial) kernel function centered at the data points. In recent work we showed that if the RBF kernel is equated to the covariance, RBF and Gaussian Process (GP) models perform a similar computation, differing in what information is assumed known in advance, and what is known at runtime. Building on the RBF-GP equivalence, we show that if the data covariance is known (or can be estimated), an RBF-inspired regression can provide data-driven “superresolution” interpolation of given data. This procedure can alternately be interpreted as a superresolution extension of eigenvector (principal component) data models, as signal sampling (function evaluation) in a discrete reproducing kernel Hilbert space (RKHS) generated by the data covariance, or as an elementary Gaussian process model in which the observations have a low-rank representation.
KeywordsRadial basis function regression Principal component analysis Gaussian process
This research is partially supported by the Japan Science and Technology Agency, CREST project. We would like to thank the reviewers, Hiroyuki Ochiai, and Ayumi Kimura. Data used in this project was obtained from mocap.cs.cmu.edu, created with funding from NSF EIA-0196217 .
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