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A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

Type of publication Peer-reviewed
Publikationsform Proceedings (peer-reviewed)
Publication date 2013
Author Auria A. , Carrillo R., Wiaux Y.,
Project Advanced signal processing on the sphere for high angular resolution diffusion magnetic resonance imaging
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Proceedings (peer-reviewed)

Title of proceedings BASP Frontiers 2013
Place Villars-sur-ollon

Open Access

URL http://infoscience.epfl.ch/record/183885
Type of Open Access Repository (Green Open Access)

Abstract

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bi-spectrum measurements. We formulate a linear version of the problem for the order-3 tensor formed by the tensor product of the signal with itself. This linear problem is regularized by standard convex \ell_1 relaxations of sparsity and low rank constraints and solved using the most advanced algorithms in convex optimization. We show preliminary results on small size synthetic images as a proof of concept.
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