1. An image processing apparatus, comprising: an information acquisition device for acquiring an eigen projective matrix generated by a projective operation from a learning image group including pairs of first quality images and second quality images different in image quality from each other, and a projective kernel tensor generated from the learning image group and the eigen projective matrix; a first sub-kernel tensor generation device for generating a first sub-kernel tensor satisfying a condition specified by a first setting from the acquired projective kernel tensor; a second sub-kernel tensor generation device for generating a second sub-kernel tensor satisfying a condition specified by a second setting from the acquired projective kernel tensor; a first sub-tensor projection device for projecting an input image as a processing target using a first projective operation utilizing the eigen projective matrix and the first sub-kernel tensor, and calculating a coefficient vector in an intermediate eigenspace; a second sub-tensor projection device for generating a modified image having a different image quality from that of the input image by projecting the calculated coefficient vector using a second projective operation utilizing the second sub-kernel tensor and the eigen projective matrix; a high image quality processing device for generating a high quality image having the same size as that of the modified image from the input image; a learning image coefficient vector acquisition device for acquiring a coefficient vector of the learning image in the intermediate eigenspace; a weight coefficient determination device for determining a weight coefficient according to a mutual relationship between the coefficient vector of the learning image in the intermediate eigenspace and the coefficient vector of the input image in the intermediate eigenspace calculated by the first sub-tensor projection device; and a synthesis device for determining an adopting ratio between a process including the first and second projective operations and a process by the high image quality processing device according to the weight coefficient, and combining the modified image and the high quality image.