Superresolution from Principal Component Models by RKHS Sampling

Conference paper
Part of the Mathematics for Industry book series (MFI, volume 18)

Abstract

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.

Keywords

Radial basis function regression Principal component analysis  Gaussian process 

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Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Victoria University and Weta Digital/JST CRESTWellingtonNew Zealand
  2. 2.OLM Digital/JST CRESTSetagaya-ku, TokyoJapan
  3. 3.Victoria UniversityWellingtonNew Zealand

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