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, wherein the processing circuitry is configured to generate a first phase image and a second phase image from which background phases are removed from the phase image by using two types of filters, acquire a function by performing function fitting on the first phase image, standardize the function to a value within a predetermined range, and generate a third phase image by blending the first phase image and the second phase image by using the value, the third phase image having the phase image from which the phase variation derived from the background magnetic field is removed by using the combination of the filters.