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Volume 30 Issue 6
Dec.  2010
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Li Min, Lu Cheng-wu, Feng Xiang-chu. A Class of Variational Model for Inverse Problem in Image Zooming[J]. Journal of Electronics & Information Technology, 2008, 30(6): 1291-1294. doi: 10.3724/SP.J.1146.2006.01508
Citation: Li Min, Lu Cheng-wu, Feng Xiang-chu. A Class of Variational Model for Inverse Problem in Image Zooming[J]. Journal of Electronics & Information Technology, 2008, 30(6): 1291-1294. doi: 10.3724/SP.J.1146.2006.01508

A Class of Variational Model for Inverse Problem in Image Zooming

doi: 10.3724/SP.J.1146.2006.01508
  • Received Date: 2006-10-09
  • Rev Recd Date: 2007-06-21
  • Publish Date: 2008-06-19
  • To a mass of computation iteration of Chambolle model in solving the inverse problem of image zooming, a class of new model that is based on Besov space is put forward. The new model translates the variational problem that is solved into a sequence based wavelet field through the equivalence between Besov semi-norm and the norm of wavelet coefficients. And the process of minimization shows that the optimization solutions of the sequence can be represented as the orthogonal projection onto wavelet field. Finally, not only the zoomed images have sharper and smooth edges, but also the details of images are kept, resulting in the naturalness. In addition, the effect of denoising is very satisfactory.
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  • Chambolle A, DeVore R A, Lee N Y, and Bradley J L.Nonlinear wavelet image processing: Variational problems,compression and noiseremoval through wavelet shrinkage[J].IEEE Transactions on Image Processing.1998, 7(3):319-335[2]Chambolle A and Bradley J L. Interpretingtranslation-invariant wavelet shrinkage as a new imagesmoothing scale space. IEEE Transactions on ImageProcessing, 2001, 10(7): 993-1000.[3]Lorenz D A. Variational denoising in Besov spaces andinterpolation of hard and soft wavelet shrinkage. University ofBremen, DFG-Schwerpunktprogramm 1114, 2003: 1-12.[4]Lorenz D A. Wavelet Shrinkage in Signal and ImageProcessing-An Investigation of Relations and Equivalences.[Ph. D thesis], University of Bremen, 2005.[5]Daubechies I and Teschke G. Wavelet based imagedecomposition by variational functionals. Proceeding-spie theInternational Society for Optical Engineering, USA, 2004,5266: 94-105.[6]Chambolle A. An algorithm for total variation minimizationand application[J].Journal of Mathematical Imaging and Vision.2004, 20(1-2):89-97[7]Guichard F and Malgouyres F. Total variation basedinterpolation. In Proceedings of the European SignalProcessing Conference, Greece, 1998, 3: 1741-1744.[8]Malgouyres F and Guichard F. Edge direction preservingimage zooming: A mathematical and numerical analysis[J].SIAM J. Numer. Anal.2001, 39 (1):1-37[9]Rockafellar R T and Roger J-B. Wets. Variational Analysis.Springer-Verlag, Berlin, Germany, 1998.
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