An Edge-Preserving Super-Precision for Simultaneous Enhancement of Spacial and Grayscale Resolutions

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 a measurement of smoothness originally used for suppression of block noises in a JPEG compressed image [Schultz & Stevenson ´94]. With a simple operator that approximates to 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, POCS based conventional method, and generalized proposed method minimizing smoothed total variation and energy of output of Laplacian