PRISM: Sparse recovery of the primordial spectrum from WMAP9 and Planck
  datasets
  The primordial power spectrum is an indirect probe of inflation or other
structure-formation mechanisms. We introduce a new method, named
\textbf{PRISM}, to estimate this spectrum from the empirical cosmic microwave
background (CMB) power spectrum. This is a sparsity-based 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 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.
