High-Performance Very Local Riesz Wavelet Bases of L₂(Rⁿ)

This is the authors' abstract. We don't add key points for this paper.

We introduce new methodologies for the construction of high-performance very local Riesz wavelet bases of L₂(Rⁿ) in arbitrarily high spatial dimension n. The localness L of the representation is measured as the sum of the volumes of the supports of the underlying mother wavelets; small localness number is one of the sought-for properties in wavelet constructions. Our constructs are very simple and they are based on our recent framelet construction methods: the CAMP scheme and the L-CAMP scheme. Within our general methodology, the subclass of piecewise-constant constructions is the most local one. It includes Riesz wavelet bases with any performance grade and in any spatial dimension. In this subclass, the Riesz wavelet basis with Jackson-type performance k (namely, with k vanishing moments) has localness score $L