1. An image processing apparatus comprising: a parameter extracting unit that extracts a parameter for expressing the degree of sharpness of each of a plurality of images, each said image obtained with a different degree of sharpness by decomposing an original image, using input image data, each parameter being an element of a diagonal matrix, said diagonal matrix obtained as a result of said decomposing of the original image, said decomposing performed by singular value decomposition; a parameter adjusting unit that adjusts each extracted parameter so as to sharpen the original image; and an image generating unit that generates an output image on the basis of the adjusted parameters, wherein, the parameter extracting unit extracts stepwise parameters expressing the degrees of sharpness of the images according to the degrees of sharpness, and the parameter adjusting unit alters the extracted parameters by at least one of: (a) pulling down an extracted parameter of an image showing a low degree of sharpness; and (b) pulling up an extracted parameter of an image showing a high degree of sharpness.