Currently, linear estimation reconstruction is the only feasible method for extracting information about spatially distributed current sources from measurements of neural magnetic fields. We present the results of a systematic study of the effect of the signal-to-noise ratio on the imaging quality of one such algorithm in over-as well as undetermined circumstances. In particular, we will discuss the necessary trade-off between the contradictory goals of a minimum norm of the reconstructed current density distribution and of a minimal deviation of the reconstructed fields from the measured fields. As an example, we show the reconstruction of a simple arrangement of two nearly parallel dipoles in two different depths inside a spherical volume conductor, discussing the differences between the computer simulation without noise and simulation with a realistic noise level.