An image quality enhancing apparatus which make a learning-type image quality enhancing method utilizing a sparse expression practical are provided. The apparatus calculates, from the feature quantity of an image, coefficients of low-image-quality base vectors expressing a feature quantity with a linear sum and generates the image with the image quality enhanced by calculating a linear sum of high-image-quality base vectors using the calculated coefficient. When calculating the coefficient, the number of base vectors with non-zero coefficients is determined, the determined number of base vectors is selected, and a solution of a coefficient matrix is calculated by assuming the coefficients of the base vectors other than the selected base vectors are zero. The amount of processes necessary for obtaining a sparse solution of a coefficient matrix can be reduced by adjusting the number of base vectors with non-zero coefficients, and a practical image quality enhancing apparatus can be realized.