1. An image processing apparatus, comprising: a storing device for storing 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, a first sub-kernel tensor generated so as to satisfy a condition specified by a first setting from a projective kernel tensor generated from the eigen projective matrix and the learning image group and specifying a relationship between the first quality image and an intermediate eigenspace and a relationship between the second quality image and the intermediate eigenspace, and a second sub-kernel tensor generated so as to satisfy a condition specified by a second setting from the projective kernel tensor; an image division device for dividing an input image of a transformation source into a plurality of divided image areas; a first sub-tensor projection device for projecting image data in the divided image area divided by the image division device using a first projective operation utilizing the eigen projective matrix and the first sub-kernel tensor, and calculating a coefficient vector in the intermediate eigenspace; a coefficient vector correction device for generating a corrected coefficient vector corrected in the intermediate eigenspace with respect to at least one divided image area among the plurality of the divided image areas on the basis of the plurality of coefficient vectors acquired by calculation by the first sub-tensor projection device with respect to a part or all of the plurality of divided image areas; and a second sub-tensor projection device for generating a modified image having a different image quality from that of the input image by projecting a coefficient vector group in the intermediate eigenspace, which includes the corrected coefficient vector generated by the coefficient vector correction device and corresponds to the divided image area, using a second projective operation utilizing the second sub-kernel tensor and the eigen projective matrix.