Quadratic Interpolation and Linear Lifting Design. (7th March 2007)

• Record Type: Journal Article
• Authors: Solé, Joel; Salembier, Philippe
• Other Names: Pesquet-Popescu Béatrice Academic Editor.
• Is Part Of: EURASIP journal on image and video processing. Volume 2007(2007)
• Publication Date: 2007-03-07
• Subjects: Image processing -- Digital techniques -- Periodicals; Digital video -- Periodicals; Traitement d'images; Vidéo numérique; Digital video; Image processing -- Digital techniques; Periodicals; Electronic journal; Electronic journals; 621.367
• DOI: 10.1155/2007/37843
• Languages: English
• ISSNs: 1687-5176

Abstract

Abstract : A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing thel 2 -norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.