24 August 2017 Optimal transport-based dictionary learning and its application to Euclid-like Point Spread Function representation
Author Affiliations +
Optimal Transport theory enables the definition of a distance across the set of measures on any given space. This Wasserstein distance naturally accounts for geometric warping between measures (including, but not exclusive to, images). We introduce a new, Optimal Transport-based representation learning method in close analogy with the usual Dictionary Learning problem. This approach typically relies on a matrix dot-product between the learned dictionary and the codes making up the new representation. The relationship between atoms and data is thus ultimately linear. By reconstructing our data as Wasserstein barycenters of learned atoms instead, our approach yields a representation making full use of the Wasserstein distance's attractive properties and allowing for non-linear relationships between the dictionary atoms and the datapoints.

We apply our method to a dataset of Euclid-like simulated PSFs (Point Spread Function). ESA's Euclid mission will cover a large area of the sky in order to accurately measure the shape of billions of galaxies. PSF estimation and correction is one of the main sources of systematic errors on those galaxy shape measurements. PSF variations across the field of view and with the incoming light's wavelength can be highly non-linear, while still retaining strong geometrical information, making the use of Optimal Transport distances an attractive prospect. We show that our representation does indeed succeed at capturing the PSF's variations.
Conference Presentation
© (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Morgan A. Schmitz, Morgan A. Schmitz, Matthieu Heitz, Matthieu Heitz, Nicolas Bonneel, Nicolas Bonneel, Fred Ngolè, Fred Ngolè, David Coeurjolly, David Coeurjolly, Marco Cuturi, Marco Cuturi, Gabriel Peyré, Gabriel Peyré, Jean-Luc Starck, Jean-Luc Starck, "Optimal transport-based dictionary learning and its application to Euclid-like Point Spread Function representation", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103940H (24 August 2017); doi: 10.1117/12.2270641; https://doi.org/10.1117/12.2270641


Cascaded models and the DQE of flat panel imagers ...
Proceedings of SPIE (May 02 2002)
Advanced sensor-simulation capability
Proceedings of SPIE (August 31 1990)
Noncoherent Optical Processing With Two-Pupil Hybrid Systems
Proceedings of SPIE (December 07 1977)
Reducing boundary distortion in image restoration
Proceedings of SPIE (October 27 1994)
Toward a mathematical framework for computational imaging
Proceedings of SPIE (November 22 2011)
Digital Image Processing And Image Synthesis In Japan
Proceedings of SPIE (July 08 1976)

Back to Top