|
|
|
A new fractal algorithm to model discrete sequences |
| Zhai Ming-Yue(翟明岳)a)†, Heidi Kuzumab), and James W. Rectorb)c) |
| a School of EE Engineering, North China Electric Power University, Beijing 102206, China; b Department of Civil Engineering, University of California, Berkeley 94530, USA; c Lawrence Berkeley Laboratory, Berkeley 94530, USA |
|
|
|
|
Abstract Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.
|
Received: 22 October 2009
Revised: 20 April 2010
Accepted manuscript online:
|
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 60972004 and 60402004). |
Cite this article:
Zhai Ming-Yue(翟明岳), Heidi Kuzuma, and James W. Rector A new fractal algorithm to model discrete sequences 2010 Chin. Phys. B 19 090509
|
| [1] |
Mandelbrot B 1982 The Fractal Geometry of Nature (San Francisco: W. H. Freeman and Co.) p31--60
|
| [2] |
Mazel D S and Hayes M H 1992 IEEE Trans. Signal Proc. 40 1724
|
| [3] |
Unser M and Thierry Blu 2007 IEEE Trans. Signal Proc. 55 1352
|
| [4] |
Unser M and Thierry Blu 2007 IEEE Trans. Signal Proc. 55 1364
|
| [5] |
Zhu X, Cheng B and Titterington D M 1994 IEE Proc-VIS Image Sign. Proc. 141 318
|
| [6] |
Barnsley M F 1988 Fractals Everywhere (New York: Academic) p205--290
|
| [7] |
Mazel D S 1994 IEEE Trans. Sign. Proc. E 42 3269
|
| [8] |
Price J R and Hayes M H 1998 IEEE Sign. Proc. Lett. 5 228
|
| [9] |
Craciunescu O I, Das S K, Poulson J M and Samulski T V 2001 IEEE Trans. Biomed. Eng. 48 462
|
| [10] |
Wang M J and Wang X Y 2009 Acta Phys. Sin. 58 1467 (in Chinese)
|
| [11] |
Yang J, Lai X M, Peng G, Bian B M and Lu J 2009 Acta Phys. Sin. 58 3008 (in Chinese)
|
| [12] |
Yang X D, Ning X B, He A J and Du S D 2008 Acta Phys. Sin. 57 1514 (in Chinese)
|
| [13] |
Gemperline M C and Siller T J 2002 J. Comput. Civil Eng. 16 184
|
| [14] |
Nath S K and Dewangan P 2002 Geophysi. Prospect. 50 341
|
| [15] |
Tirosh S, Van De Ville D and Unser M 2006 IEEE Trans. Image Proc. 15 2616
|
| [16] |
Bouboulis P and Dalla L 2007 J. Math. Anal. Appl. bf 336 919
|
| [17] |
Li X F and Li X F 2008 Chin. Phys. Lett. 25 1157
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
