This paper extends the minimum-norm least-squares inverse approach to a local spherical model for the conductivity geometry of the human head. In simulations of cortical activity of the human brain, the magnetic field pattern across the scalp is interpreted with prior knowledge of anatomy, and the properties of intraneuronal current flow to yield a unique magnetic source image across a portion of cerebral cortex. Influences on the quality of magnetic source images from the noise in measurements, the position error in determining the image surface, and the number of sensors are evaluated in detail.