[IPOL discuss] [IPOL announce] new article: L1-Norm Redundant Delaunay Phase Unwrapping and Gradient Correction

[announcements about the IPOL journal]

A new article is available in IPOL: https://www.ipol.im/pub/art/2025/583/

Alexandre Achard-de Lustrac, Roland Akiki, Axel Davy, and Jean-Michel 
Morel,
L1-Norm Redundant Delaunay Phase Unwrapping and Gradient Correction,
Image Processing On Line, 15 (2025), pp. 108–162.
https://doi.org/10.5201/ipol.2025.583

Abstract
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 [M. Constantini, A Novel Phase Unwrapping Method Based on 
Network Programming, IEEE Transactions on Geoscience and Remote Sensing, 
1998] and [M. Constantini et al., A general formulation for redundant 
integration of finite differences and phase unwrapping on a sparse 
multidimensional domain, IEEE Transactions on Geoscience and Remote 
Sensing, 2012], 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 L1-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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