Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator.

Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley · Proc Natl Acad Sci U S A · 2014

basic_science · Level V

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Abstract

This paper describes an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves, that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities.