  We present a concept study on weak lensing map reconstruction through the
cosmic magnification effect in galaxy number density distribution. We propose a
minimal variance linear estimator to minimize both the dominant systematical
and statistical errors in the map reconstruction. It utilizes the distinctively
different flux dependences to separate the cosmic magnification signal from the
overwhelming galaxy intrinsic clustering noise. It also minimizes the shot
noise error by an optimal weighting scheme on the galaxy number density in each
flux bin. Our method is in principle applicable to all galaxy surveys with
reasonable redshift information. We demonstrate its applicability against the
planned Square Kilometer Array survey, under simplified conditions. Weak
lensing maps reconstructed through our method are complementary to that from
cosmic shear and CMB and 21cm lensing. They are useful for cross checking over
systematical errors in weak lensing reconstruction and for improving
cosmological constraints.
