tailieunhanh - Báo cáo hóa học: " Research Article Quadratic Interpolation and Linear Lifting Design"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Quadratic Interpolation and Linear Lifting Design | Hindawi Publishing Corporation EURASIP Journal on Image and Video Processing Volume 2007 Article ID 37843 11 pages doi 2007 37843 Research Article Quadratic Interpolation and Linear Lifting Design Joel Sole and Philippe Salembier Department of Signal Theory and Communications Technical University of Catalonia UPC Jordi Girona 1-3 EdificiD5 Campus Nord Barcelona 08034 Spain Received 11 August 2006 Revised 18 December 2006 Accepted 28 December 2006 Recommended by Beatrice Pesquet-Popescu 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 1 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. Copyright 2007 J. Sole and P. Salembier. 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. 1. INTRODUCTION The lifting scheme 1 is a method to create biorthogonal wavelet filters from other ones. Despite the amount of research effort dedicated to the design and optimization of lifting filters since the scheme was proposed many works . 2-4 that contribute ideas to improve existing lifting steps with new