Varilets: Additive Decomposition, Topological Total Variation, and Filtering of Scalar Fields
Year: 2015
Type: preprint
Abstract: Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D total variation. A varilet basis is a collection of piecewise monotone functions { $g_i$ |i = 1...n}, called varilets, such that every linear combination $\sum a_ig_i$ has topological total variation $\sum |a_i|$. A varilet transform for $f$ is a varilet basis for which $f =\sum α_ig_i$. Filtered versions of $f$ result from altering the coefficients $α_i$.
Source: arXiv (Cornell University)
Author: Brooks, Martin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1741069098