Edge noise in thin-film magnetic recording media is modeled using a planar array of hexagonal grains with long-range magnetostatic interactions as well as possible nearest-neighbor exchange interactions. The Landau-Lifschitz equations of motion with infinite damping are used to find the magnetization configurations. dc-erased track edges were simulated in a standstill manner using a gap centerline approximation to a realistic three-dimensional head field. The intergranular exchange coupling was varied keeping the medium parameter Mr/Hc constant. Magnetization patterns and modeled Fresnel images demonstrate the effects of exchange coupling on the ripple and vortex structures in the presence of the edge-field gradient. The fluctuation of the downtrack magnetization is a maximum at the edge of the track, where the local average of the magnetization itself is near zero.