Multiscale blind source separation

We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an ε-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the Read more…

Minimax estimation in linear models with unknown finite alphabet design

We provide minimax theory for joint estimation of F and ω in linear models Y=Fω+Z where the parameter matrix ω and the design matrix F are unknown but the latter takes values in a known finite set. This allows to separate F and ω, a task which is not doable, in general. We obtain in Read more…

Identifiability for blind source separation of multiple finite alphabet linear mixtures.

We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a detailed treatment of the case of a single linear mixture. Notably, our identifiability analysis applies also to the case of unknown Read more…