The Marr Conjecture and Uniqueness of Wavelet Transforms

Abstract

The inverse question of identifying a function from the nodes (zeroes) of its wavelet transform arises in a number of fields. These include whether the nodes of a heat or hypoelliptic equation solution determine its initial conditions, and in mathematical vision theory the Marr conjecture, on whether an image is mathematically determined by its edge information. We prove a general version of this conjecture by reducing it to the moment problem, using a basis dual to the Taylor monomial basis $x^{\alpha }$ on ${\mathbb{R}}^n$.

52 pages, 4 figures

References in corpus (1)

• Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2