On compactly supported discrete radial wavelets in $L^2(\mathbb{R}^2)$ and application in Tomography

TL;DR

This paper introduces a new method for designing compactly supported radial wavelets in two dimensions using 1D Daubechies wavelets, with applications demonstrated in tomography.

Contribution

A novel approach to constructing compactly supported radial wavelets in $L^2( eal^2)$ from 1D Daubechies wavelets, including a multiresolution reconstruction formula.

Findings

Effective in localized operations like reconstruction and enhancement

Demonstrated usefulness in tomography applications

Provides a multiresolution framework for radial wavelets

Abstract

Radially symmetric wavelets possessing multiresolution framework are found to be useful in different fields like Pattern recognition, Computed Tomography (CT) etc. The compactly supported wavelets are known to be useful for localized operations in applications such as reconstruction, enhancement etc. In this work we introduce a novel way of designing compactly supported radial wavelets in $L^2(\mathbb{R}^2)$ from a 1D Daubechies wavelets and obtain a reconstruction formula possessing multiresolution framework. Further, we demonstrate the usefulness of our radial wavelets in Tomography.