1. A magnetic-resonance imaging apparatus comprising acquiring circuitry configured to acquire a magnetic resonance signal that is generated from a subject; and processing circuitry configured to create a phase image based on the magnetic resonance signal, set a combination of a plurality of filters that are used to remove a phase variation derived from a background magnetic field according to a region in the phase image, and remove a phase variation derived from the background magnetic field from the phase image by using the combination of the filters.