Relation between the noise-free average unsigned vertical flux density (vertical axis, in the text denoted B_ave) and the corresponding noise-affected flux density (horizontal axis, in the text denoted B_app), for two values of σ for the noise distribution, 18 and 34 G. The solid curves are obtained through numerical convolution of PDFs that are representative of quiet-sun magnetic fields (as derived from Hinode analysis) with Gaussian noise distributions, while the dashed curves are analytical representations of the solid curves in terms of Eqs. (3) and (4).