To cite this version:Cécile Chenot, Jérôme Bobin. Blind separation of sparse sources in the presence of outliers. Signal Processing, Elsevier, 2017, 138, pp.233 -243 robustness of this new algorithm with respect to aberrant outliers on a wide range of blind separation instances. In contrast to current robust BSS methods, the rAMCA algorithm is shown to perform very well when the number of observations is close or equal to the number of sources.

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Abstract. The primordial power spectrum is an indirect probe of inflation or other structureformation mechanisms. We introduce a new method, named PRISM, to estimate this spectrum from the empirical cosmic microwave background (CMB) power spectrum. This is a sparsitybased inversion method, which leverages a sparsity prior on features in the primordial spectrum in a wavelet dictionary to regularise the inverse problem. This non-parametric approach is able to reconstruct the global shape as well as localised features of the primordial spectrum accurately and proves to be robust for detecting deviations from the currently favoured scale-invariant spectrum. We investigate the strength of this method on a set of WMAP nine-year simulated data for three types of primordial spectra and then process the WMAP nine-year data as well as the Planck PR1 data. We find no significant departures from a near scale-invariant spectrum.

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