In this paper, we propose a method that recovers a smooth high-resolution image from several blurred and roughly quantized low-resolution images. For compensation of the quantization effect we introduce measurements of smoothness, Huber function that is originally used for suppression of block noises in a JPEG compressed image [Schultz & Stevenson '94] and a smoothed version of total variation. With a simple operator that approximates the convex projection onto constraint set defined for each quantized image [Hasegawa et al. '05], we propose a method that minimizes these cost functions, which are smooth convex functions, over the intersection of all constraint sets, i. e. the set of all images satisfying all quantization constraints simultaneously, by using hybrid steepest descent method [Yamada & Ogura '04]. Finally in the numerical example we compare images derived by the proposed method, Projections Onto Convex Sets (POCS) based conventinal method, and generalized proposed method minimizing energy of output of Laplacian.