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The primordial power spectrum is an indirect probe of inflation or otherstructure-formation mechanisms. We introduce a new method, named\textbf{PRISM}, to estimate this spectrum from the empirical cosmic microwavebackground (CMB) power spectrum. This is a sparsity-based inversion method,which leverages a sparsity prior on features in the primordial spectrum in awavelet dictionary to regularise the inverse problem. This non-parametricapproach is able to reconstruct the global shape as well as localised featuresof spectrum accurately and proves to be robust for detecting deviations fromthe currently favoured scale-invariant spectrum. We investigate the strength ofthis method on a set of WMAP nine-year simulated data for three types ofprimordial spectra and then process the WMAP nine-year data as well as thePlanck PR1 data. We find no significant departures from a near scale-invariantspectrum.

PRISM: Sparse recovery of the primordial spectrum from WMAP9 and Planck datasets