1. A magnetic resonance imaging apparatus comprising: a data acquisition unit configured to acquire plural pieces of data for imaging and plural pieces of projection data for obtaining breath levels of an object respectively from the object by continuously applying a radio frequency pulse train to the object with a constant interval; a correction unit configured to perform motion correction of the plural pieces of the data with using the breath levels of the object obtained based on the plural pieces of the projection data; a data sorting unit configured to sort the plural pieces of the data after the motion correction into a cardiac time phase order based on electrocardiographic information of the object; and an image reconstruction unit configured to reconstruct three dimensional image data based on the plural pieces of the data sorted in the cardiac time phases after the motion correction.