1. A coefficient learning apparatus comprising: student-image generation means for generating a student image, which has a quality degraded from the quality of a teacher image in accordance with a plurality of deterioration model equations each corresponding to one of the plurality of deterioration types, from said teacher image; class classification means for sequentially setting each of pixels in said teacher image as a pixel of interest and generating a class for said pixel of interest from the values of pixels in said student image located at positions corresponding to the position of said pixel of interest and peripheral positions surrounding said position of said pixel of interest; weight computation means for computing a weight of a constraint condition equation for at least some pixels in said teacher image based on the sum of feature quantities for said each class, said feature quantity representing a relation between said pixels and adjacent pixels in said teacher image under said deterioration model equation used for finding the values of pixels in said student image from the values of pixels located at positions corresponding to the position of said pixel of interest and peripheral positions surrounding said position of said pixel of interest; and processing-coefficient generation means for generating a prediction coefficient to predict the value of said pixel of interest in said teacher image by carrying out a computation process applying to said plurality of pixels in student image for said each deterioration type and each class on the basis of a determinant including said deterioration equation and a weighted constraint condition equation.