Primordial Power Spectrum from Lensed CMB Temperature Spectrum using
  Iterative Delensing
  We address a current caveat in the deconvolution of the Primordial Power
Spectrum (PPS), from observed Cosmic Microwave Background (CMB) temperature
anisotropy, in the presence of weak lensing of the CMB by the large scale
structure (LSS) in the Universe. We propose a modification to the popular
Richardson-Lucy (RL) deconvolution algorithm used in the context of
reconstructing a free-form PPS, $P_R(k)$ from observed lensed CMB temperature
anisotropy power spectrum $\widetilde{C}_{\ell}^{TT}$. We show that the
modified RL algorithm works in the context of a non-linear convolution problem,
such as in the case of weak lensing. The Non-Linear Iterative Richardson-Lucy
(NIRL) algorithm is successful at both convergence, as well as fidelity, in
reconstructing features in some underlying PPS. This makes PPS reconstruction
efforts more robust in the context of lensed CMB temperature observations. No
prior assumptions on the PPS are involved during the iterative delensing
process, and distinct improvement is noted over a power-law template based
delensing approach used earlier, at the cost of moderately increased
computational cost due to the NIRL reconstruction.
