On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters

Fredrik Andersson (1) , Magnus Carlsson (1) , Herwig Wendt (2, 3)

1 Skane University Hospital [Lund]
2 IRIT-SC - Signal et Communications
3 CNRS - Centre National de la Recherche Scientifique

We study the problem of decomposing a measured signal as a sum of decaying exponentials. There is a direct connection to sums of these types and positive semi-definite (PSD) Hankel matrices, where the rank of these matrices equals the number of exponentials. We propose to solve the identification problem by forming an optimization problem with a misfit function combined with a rank penalty function that also ensures the PSD-constraint. This problem is non-convex, but we show that it is possible to compute the minimum of an explicit closely related convexified problem. Moreover, this minimum can be shown to often coincide with the minimum of the original non-convex problem, and we provide a simple criterion that enables to verify if this is the case.

Mots clés: Low rank approximation; Structured matrices; Fixed-point algorithms

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Fredrik Andersson, Magnus Carlsson, Herwig Wendt. On a fixed-point algorithm for structured low-rank approximation and estimation of half-life parameters. 24th European Signal Processing Conference (EUSIPCO 2016), Aug 2016, Budapest, Hungary. pp. 326-330. ⟨hal-01447346⟩