  The primordial power spectrum describes the initial perturbations that seeded
the large-scale structure we observe today. It provides an indirect probe of
inflation or other structure-formation mechanisms. In this letter, we recover
the primordial power spectrum from the Planck PR1 dataset, using our recently
published algorithm PRISM. PRISM is a sparsity-based inversion method, that
aims at recovering features in the primordial power spectrum from the empirical
power spectrum of the cosmic microwave background (CMB). This ill-posed inverse
problem is regularised using a sparsity prior on features in the primordial
power spectrum in a wavelet dictionary. Although this non-parametric method
does not assume a strong prior on the shape of the primordial power spectrum,
it is able to recover both its general shape and localised features. As a
results, this approach presents a reliable way of detecting deviations from the
currently favoured scale-invariant spectrum. We applied PRISM to 100 simulated
Planck data to investigate its performance on Planck-like data. We also tested
the algorithm's ability to recover a small localised feature at $k \sim 0.125$
Mpc$^{-1}$, which caused a large dip at $\ell \sim 1800$ in the angular power
spectrum. We then applied PRISM to the Planck PR1 power spectrum to recover the
primordial power spectrum. We find no significant departures from the fiducial
Planck PR1 near scale-invariant primordial power spectrum with
$A_s=2.215\times10^{-9}$ and $n_s = 0.9624$.
