  While the simplest inflationary models predict the primordial perturbations
to be near scale-invariant, the primordial power spectrum (PPS) can exhibit
oscillatory features in many physically well-motivated models. We search for
hints of such features via free-form reconstructions of the PPS based on
\textit{Planck} 2018 CMB temperature and polarization anisotropies. In order to
robustly invert the oscillatory integrals and handle noisy unbinned data, we
draw inspiration from image analysis techniques. In previous works, the
Richardson-Lucy deconvolution algorithm for deblurring images has been modified
for reconstructing PPS from the CMB temperature angular power spectrum. We
extensively develop the methodology by including CMB polarization and
introducing two new regularization techniques, also inspired by image analysis
and adapted for our cosmological context. Regularization is essential for
improving the fit to the temperature and polarization channels (TT, TE and EE)
simultaneously without sacrificing one for another. The reconstructions we
obtain are consistent with previous findings from temperature-only analyses. We
evaluate the statistical significance of the oscillatory features in our
reconstructions using mock data and find the observations to be consistent with
having a featureless PPS. The machinery developed here will be a complimentary
tool in the search for features with upcoming CMB surveys. Our methodology also
shows competitive performance in image deconvolution tasks, which have various
applications from microscopy to medical imaging.
