Weak lensing reconstruction through cosmic magnification I: a minimal variance map reconstruction

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.