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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 denoising the corrupted image. The same system can compare a noisy input image with a stored image and make a matching decision using magnetic tunnel junctions. These tasks are executed at ultrahigh speeds ( ~ 2 ns for a 512 ×512 pixel image).