Weak Lensing Magnification Reconstruction with the Modified Internal
  Linear Combination Method
  Measuring weak lensing cosmic magnification signal is very challenging due to
the overwhelming intrinsic clustering in the observed galaxy distribution. In
this paper, we modify the Internal Linear Combination (ILC) method to
reconstruct the lensing signal with an extra constraint to suppress the
intrinsic clustering. To quantify the performance, we construct a realistic
galaxy catalogue for the LSST-like photometric survey, covering $20\,000\
\deg^2$ with mean source redshift at $z_s\sim 1$. We find that the
reconstruction performance depends on the width of the photo-z bin we choose.
Due to the correlation between the lensing signal and the source galaxy
distribution, the derived signal has smaller systematic bias but larger
statistical uncertainty for a narrower photo-z bin. We conclude that the
lensing signal reconstruction with the Modified ILC method is unbiased with a
statistical uncertainty $<5\%$ for bin width $\Delta z^P = 0.2$.
