Top panel: comparison between the usual LSD profile, the scaled cross-correlation function and the LSD profile reconstructed using regularization. These profiles are obtained from a simulated S/N = 15 spectrum, containing 500 randomly distributed scaled lines with a characteristic Stokes V S-shaped signature. Profiles are shifted vertically for display purpose. The indicated signal-to-noise ratio is inferred from the pixel scatter in the regions on both sides of the profile. Bottom panel: the difference between LSD profiles and the corresponding CCF.