一类针对图像放大中反问题的变分模
doi: 10.3724/SP.J.1146.2006.01508
A Class of Variational Model for Inverse Problem in Image Zooming
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摘要: 在解决图像放大中的反问题时，Chambolle变分模型需要大量的计算迭代。针对这种不足，该文提出一类新的基于Besov空间的变分模型来解决相应问题。利用Besov半范数与小波系数范数的等价性，新模型将所求解的变分问题完全转化为基于小波域的变分序列，其极小化过程证明这些序列的最优解都可以表示为基于小波域的正交投影。实验结果表明：新方法处理后的放大图像边缘轮廓清晰、光滑，有意义的细节特征得到保留，去噪效果令人满意。Abstract: 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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