Performance asymptotique d'estimateurs de modèles CP avec facteurs structurés

Abstract : The canonical polyadic decomposition (CPD) of a tensor, also known as Candecomp/Parafac, is very useful for numerous applications. Structured CPDs, i.e. with Toeplitz, circulant, or Hankel factor matrices, are often encountered in signal processing applications. Specialized algorithms were recently proposed for estimating the parameters of structured CPD. A closed-form expression of the Cramér-Rao bound (CRB) is derived for the estimated CPD parameters, when the observed tensor is corrupted with an additive i.i.d. circular Gaussian noise. The proposed CRB expression is used to asses the statistical efficiency of two estimation algorithms by means of simulation results in the cases of third-order tensors having three circulant factors on one hand, and an Hankel factor on the other hand.
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Maxime Boizard, José Henrique de M Goulart, Remy Boyer, Gérard Favier, Pierre Comon. Performance asymptotique d'estimateurs de modèles CP avec facteurs structurés. XXVème colloque GRETSI (GRETSI 2015), Sep 2015, Lyon, France. 4 p. ⟨hal-01169880⟩

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