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  • Research Article
  • Open Access

Quadratic Interpolation and Linear Lifting Design

EURASIP Journal on Image and Video Processing20072007:037843

  • Received: 11 August 2006
  • Accepted: 28 December 2006
  • Published:


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 the l2-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.


  • Equality Constraint
  • Quadratic Function
  • Interpolation Method
  • Convex Optimization
  • Linear Constraint


Authors’ Affiliations

Department of Signal Theory and Communications, Technical University of Catalonia (UPC), Jordi Girona 1–3, Edifici D5, Campus Nord, Barcelona, 08034, Spain


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© J. Solé and P. Salembier 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.