  A circular magnetic disk with biaxial magnetocrystalline anisotropy has four
stable magnetization states which can be used to encode a pixel's shade in a
black/gray/white image. By solving the Landau-Lifshitz- Gilbert equation, we
show that if moderate noise deflects the magnetization slightly from a stable
state, it always returns to the original state, thereby automatically
de-noising the corrupted image. The same system can compare a noisy input image
with a stored image and make a matching decision using magneto-tunneling
junctions. These tasks are executed at ultrahigh speeds (~2 ns for a
512\times512 pixel image).
