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分形小波变换编码有限步迭代收敛的讨论

马波 裘正定

马波, 裘正定. 分形小波变换编码有限步迭代收敛的讨论[J]. 电子与信息学报, 2000, 22(3): 416-422.
引用本文: 马波, 裘正定. 分形小波变换编码有限步迭代收敛的讨论[J]. 电子与信息学报, 2000, 22(3): 416-422.
Ma Bo, Qiu Zhengding. THE DISCUSSION ABOUT FINITE ITERATION CONVERGENCE OF FRACTAL WAVELET TRANSFORMATION[J]. Journal of Electronics and Information Technology, 2000, 22(3): 416-422.
Citation: Ma Bo, Qiu Zhengding. THE DISCUSSION ABOUT FINITE ITERATION CONVERGENCE OF FRACTAL WAVELET TRANSFORMATION[J]. Journal of Electronics and Information Technology, 2000, 22(3): 416-422.

分形小波变换编码有限步迭代收敛的讨论

THE DISCUSSION ABOUT FINITE ITERATION CONVERGENCE OF FRACTAL WAVELET TRANSFORMATION

  • 摘要: 本文首先证明了小波域中去除了均值的分形小波变换算子M可以在有限步迭代中逼近其固定点,从而使得分形小波变换编码可以在不是完全压缩的条件下完成收敛;然后对这种放宽了收敛条件的编码算法给出了压缩因子的一个上界,并据此对Fisher提出的终值压缩性思想作出了有效的解释。
  • Davis G M. A wavelet-based analysis of fractal image compression .IEEE Trans. on Image Processing, 1998,72, 7(2) :141-154.[2] Simon B. Explicit link between local fractal transform and multiresolusion transform. Proceedings of Signal Processing, edited by J. Storer. IEEE Computer Society Press, 1995,362-366.[2]Rinaldo R, Calvagno G. Image coding by block prediction of multiresolution subimages [J].IEEE Trans. on Image Processing.1995,-4(7):909-920[3]Fisher Y, Jacobs E W, Boss R Do. Fractal Image Compression Using Iterated Transforms in Image and Text Compression (J. A. Storer, ed.) Kluwer Academic Publishers, 1992, ch. 2:35-61.[4]Barnsley M F, Ervin V, Hardin D, Lancaster J. Solution of an inverse problem for fractals and other sets [J].Proc. of the National Academy of Science of the USA.1986, 83(2):1975-1977[5]Forte B, Vrscay E R. Solving the inverse problem for function/image approximation using iterated function systems .Fractals, 1994,23, 2(3) :335-346.[6]蒋正新.矩阵理论及其应用.北京:北京航空航天大学出版社,1988,第四章:207-211.[7]Lundheim L M. A discrete framework for fractal signal modeling in fractal compression: Theory and Application to Digital Images, Fisher,Y., Ed. New York: Springer-Verlag, 1994: 250-277.[8]马波,裘正定. 小波变换的分形特性,北京:铁道学报, 1998,(6):1-7.[9]秦前清,杨宗凯.实用小波分析.西安:西安电子科技大学出版社,1995,第二章,22页.[10]Antonini M, M Barlaud, I Daubechies. Image coding using wavelet transform[J].IEEE Trans. on Image Processing.1992,1(4):205-220
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出版历程
  • 收稿日期:  1998-08-19
  • 修回日期:  1999-02-12
  • 刊出日期:  2000-05-19

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