Pré-Publication, Document De Travail Année : 2025

L1-Norm Redundant Delaunay Phase Unwrapping and Gradient Correction

Résumé

This article deals with arrays of real numbers which have been reduced modulo 2h into the interval [-h, h] where h > 0 is a positive real number. Such an array is said to be wrapped modulo 2h. Often, the elements of these arrays correspond to values observed at points in an image-like 2D space which are connected by a graph structure. The process of retrieving the original array from which the wrapped image originates is called unwrapping. Of course, the wrapping process is not one-to-one, and the quality of the recovered unwrapped version depends on the smoothness of the original array. The goal of unwrapping is to define a most plausible left inverse (as will be defined in a precise way) to the non-injective modulation operator mod 2h using heuristic arguments and regularity assumptions on the original signal. Following the guidelines described in [3] and [5], this is made possible by correcting an approximate gradient into a global gradient using either linear programming or, in some cases, minimum-cost flow techniques to solve an L 1 -norm optimization problem. Such a gradient-correcting technique can also be used in general for finding a most plausible gradient and reconstructing a signal. The online demo associated with this paper implements the aforementioned methods.
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hal-04937913 , version 1 (10-02-2025)

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  • HAL Id : hal-04937913 , version 1

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Alexandre Achard-de Lustrac, Roland Akiki, Axel Davy, Jean-Michel Morel. L1-Norm Redundant Delaunay Phase Unwrapping and Gradient Correction. 2025. ⟨hal-04937913⟩
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