1. An image data restoration apparatus for restoring still image data acquired by capturing a subject image with an imaging element, on a basis of blur information regarding blur in a one-dimensional direction of the imaging element upon image capturing, the apparatus comprising: an image data recovering unit that multiplies the still image data and a recovery matrix to recover ideal image data, wherein: the recovery matrix is used to recover, from the still image data, the ideal image data which is acquired upon capturing the subject image in a state where there is no blur based on the blur information, and the recovery matrix is a pseudo inverse matrix of a blur matrix that represents spread in the one-dimensional direction of the ideal image data due to the blur based on the blur information; a noise computing unit that computes a plurality of types of noises that derive from the recovery matrix, the plurality of types of noises being periodically superimposed on the image data recovered by the image data recovering unit toward the one-dimensional direction; and a noise eliminating unit that eliminates the noise computed by the noise computing unit, from the image data recovered by the image data recovering unit, wherein: the recovery matrix is an inverse matrix of an approximate matrix, the approximate matrix being obtained by approximating the blur matrix, the approximate matrix being defined so as to extrapolate a predetermined value into values of image data that spreads from an end portion of the ideal image data to an outer side in the one-dimensional direction according to the blur based on the blur information, and the noise computing unit computes the plurality of types of noises on a basis of (i) noise period information regarding a noise superimposition period of each of the plurality of types of noises, the noise period information being computed according to a product of the recovery matrix and the blur matrix, (ii) the image data recovered by the image data recovering unit, and (iii) the still image data.