Digital Deblurring of CMB Maps:
Performance and Efficient Implementation
R. Vio, J. Nagy, L. Tenorio, P. Andreani, C. Baccigalupi
and W. Wamsteker
Digital deblurring of images is an important problem that arises in
multifrequency observations of the Cosmic Microwave Background (CMB)
where, because of the width of the point spread functions (PSF), maps
of different frequencies suffer a different loss of spatial
resolution. Deblurring is useful for various reasons: first, it helps
restore some of the signal's high frequencies lost through the
smoothing effect of the instrument's PSF; second, emissions at various
frequencies observed with different resolutions can be better studied
on a comparable resolution; third, map-based component separation
algorithms require input maps with similar level of degradation. Here
we consider the performance of Tikhonov deblurring of noisy maps with
applications to {\it PLANCK}. Compared to deblurring in frequency
space, Tikhonov deblurring in real space allows the efficient
implementation of algorithms in a wide range of applications that
include deblurring with spatially dependent PSF, and deblurring with
white or correlated noise. We discuss the use of the Tikhonov
methodology in practical applications and provide details for an
efficient implementation of the algorithms. Its performance is tested
on simulated CMB maps; results indicate the possibility of a
substantial gain in angular resolution. Matlab code is made available.