In this paper a novel method for image superresolution is proposed. The primary theory is proved that the 2-dimension image data can be approximated by the products of 1-dimension functions whose variables are separated from the image' s variables. Therefore

the image superresolution can proceed conveniently through the 1-dimension superresolution. Concretely

the digital image (M×N) can be expressed by the summation of the products ofM-dimension vectors andN-dimension vectors. So the image superresolution process can be converted to the M-dimension vector processing and theN-dimension vector processing easily. Thus the method is based on the eigenvectors. In the mean-square-error sense

this expression or decomposition is optimum. It is also proved to be identical with the literature[3] when the hits go to infinite. At last the applications verify the theoretical result. Namely

this method has the better results and can reduce the calculations because the image can be adjusted adaptively and be expressed by the less parameters. In addition

this method can also be applied to other fields of image processing and the information processing of the great-capacity data.