Weak lensing power spectrum reconstruction by counting galaxies.-- I:
  the ABS method
  We propose an Analytical method of Blind Separation (ABS) of cosmic
magnification from the intrinsic fluctuations of galaxy number density in the
observed galaxy number density distribution. The ABS method utilizes the
different dependences of the signal (cosmic magnification) and contamination
(galaxy intrinsic clustering) on galaxy flux, to separate the two. It works
directly on the measured cross galaxy angular power spectra between different
flux bins. It determines/reconstructs the lensing power spectrum analytically,
without assumptions of galaxy intrinsic clustering and cosmology. It is
unbiased in the limit of infinite number of galaxies. In reality the lensing
reconstruction accuracy depends on survey configurations, galaxy biases, and
other complexities, due to finite number of galaxies and the resulting shot
noise fluctuations in the cross galaxy power spectra. We estimate its
performance (systematic and statistical errors) in various cases. We find that,
stage IV dark energy surveys such as SKA and LSST are capable of reconstructing
the lensing power spectrum at $z\simeq 1$ and $\ell\la 5000$ accurately. This
lensing reconstruction only requires counting galaxies, and is therefore highly
complementary to the cosmic shear measurement by the same surveys.
