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

Hiroshi HASEGAWA  Toshinori OHTSUKA  Isao YAMADA  Kohichi SAKANIWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.2   pp.673-681
Publication Date: 2008/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.2.673
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Image
super-resolution,  Huber function,  total variation,  set-theoretic approach,  outer approximation,  hybrid steepest descent method,  

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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.