High-Performance Very Local Riesz Wavelet Bases of $L_2({\mathbb{R}^n})

We introduce new methodologies for the construction of high-performance very local Riesz wavelet bases of $L_2({\mathbb{R}^n})$ 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