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 a 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 each pixel of interest from values of pixels in said student image located at positions corresponding to the position of each pixel of interest and peripheral positions surrounding said position of each pixel of interest; weight computation means for computing a weight of each constraint condition equation of a plurality of constraint condition equations 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 at least some pixels and adjacent pixels in said teacher image under each deterioration model equation used for finding the values of pixels in said student image from values of pixels located at positions corresponding to the position of each pixel of interest and peripheral positions surrounding said position of each pixel of interest; and processing-coefficient generation means for generating a prediction coefficient to predict a value of each pixel of interest in said teacher image by carrying out a computation process applying to a plurality of pixels in the student image for each deterioration type and each class on the basis of a determinant including each deterioration model equation and each constraint condition equation.