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arXiv · 1401.0542

The Marr Conjecture and Uniqueness of Wavelet Transforms

Ben Allen·Mark Kon
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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 $x^α$ on $\mathbb {R}^n$.

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Ben Allen, Mark Kon. 2015-04-15. The Marr Conjecture and Uniqueness of Wavelet Transforms. https://arxiv.org/abs/1401.0542

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