  The cosmic microwave background (CMB) power spectrum is a powerful
cosmological probe as it entails almost all the statistical information of the
CMB perturbations. Having access to only one sky, the CMB power spectrum
measured by our experiments is only a realization of the true underlying
angular power spectrum. In this paper we aim to recover the true underlying CMB
power spectrum from the one realization that we have without a need to know the
cosmological parameters. The sparsity of the CMB power spectrum is first
investigated in two dictionaries; Discrete Cosine Transform (DCT) and Wavelet
Transform (WT). The CMB power spectrum can be recovered with only a few
percentage of the coefficients in both of these dictionaries and hence is very
compressible in these dictionaries. We study the performance of these
dictionaries in smoothing a set of simulated power spectra. Based on this, we
develop a technique that estimates the true underlying CMB power spectrum from
data, i.e. without a need to know the cosmological parameters. This smooth
estimated spectrum can be used to simulate CMB maps with similar properties to
the true CMB simulations with the correct cosmological parameters. This allows
us to make Monte Carlo simulations in a given project, without having to know
the cosmological parameters. The developed IDL code, TOUSI, for Theoretical
pOwer spectrUm using Sparse estImation, will be released with the next version
of ISAP.
