1. An image processing device characterized by comprising: an information acquisition unit configured to acquire an eigenprojection matrix generated by a projection computation from a studying image group including at least one of an image pair formed by high frequency components of a first-quality image and a second-quality image with different image qualities and an image pair formed by the high frequency components and medium frequency components of the first-quality image and the second-quality image, and to acquire a projection core tensor generated from the studying image group and the eigenprojection matrix; a first sub-core tensor generation unit configured to generate a first sub-core tensor corresponding to a condition specified by a first setting from the acquired projection core tensor; a second sub-core tensor generation unit configured to generate a second sub-core tensor corresponding to a condition specified by a second setting from the acquired projection core tensor; a filtering unit configured to generate a low frequency component control image in which high frequency components or the high frequency components and medium frequency components of an input image to be processed are extracted; a first subtensor projection unit configured to project the low frequency component control image by a first projection computation using the eigenprojection matrix and the first sub-core tensor to calculate a coefficient vector in an intermediate eigenspace; a second subtensor projection unit configured to project the calculated coefficient vector by a second projection computation using the second sub-core tensor and the eigenprojection matrix to generate a projection image from the low frequency component control image; an image conversion unit configured to generate a conversion image with an image quality different from the input image; and an addition unit configured to add the projection image and the conversion image.