Context :

Aims : The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today , and thereby provides an indirect probe of inflation or other structure-formation mechanisms .
Here , we introduce a new method to estimate this spectrum from the empirical power spectrum of cosmic microwave background ( CMB ) maps .

Methods : A sparsity-based linear inversion method , coined PRISM , is presented .
This technique leverages a sparsity prior on features in the primordial power spectrum in a wavelet basis to regularise the inverse problem .
This non-parametric approach does not assume a strong prior on the shape of the primordial power spectrum , yet is able to correctly reconstruct its global shape as well as localised features .
These advantages make this method robust for detecting deviations from the currently favoured scale-invariant spectrum .

Results : We investigate the strength of this method on a set of WMAP 9-year simulated data for three types of primordial power spectra : a nearly scale-invariant spectrum , a spectrum with a small running of the spectral index , and a spectrum with a localised feature .
This technique proves to easily detect deviations from a pure scale-invariant power spectrum and is suitable for distinguishing between simple models of the inflation .
We process the WMAP 9-year data and find no significant departure from a nearly scale-invariant power spectrum with the spectral index n _ { s } = 0.972 .

Conclusions : A high resolution primordial power spectrum can be reconstructed with this technique , where any strong local deviations or small global deviations from a pure scale-invariant spectrum can easily be detected .