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A NEW FRACTAL INTERPOLATION ALGORITHM AND ITS APPLICATIONS TO SELF-AFFINE SIGNAL RECONSTRUCTION

School of Electrical and Electronic Engineering, North China Electric Power University, 17# Li Hua ChangPing, Beijing 102206, China

Corresponding author.

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JUAN LUIS FERNÁNDEZ-MARTÍNEZ

Mathematics Department, University of Oviedo, Oviedo, Spain

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, and

JAMES W. RECTOR

Department of Civil Engineering, University of California, Berkeley, CA 94530, USA

Lawrence Berkeley National Laboratory, Berkeley, CA 94530, USA

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https://doi.org/10.1142/S0218348X11005427Cited by:13 (Source: Crossref)

Abstract

A new fractal interpolation method called PPA (Pointed Point Algorithm) based on IFS is proposed to interpolate the self-affine signals with the expected interpolation error, solving the problem that the ordinary fractal interpolation can't get the value of any arbitrary point directly, which has not been found in the existing literatures. At the same time, a new method to calculate the vertical scaling factors is proposed based on the genetic algorithm, which works together with the PPA algorithm to get the better interpolation performance. Experiments on the theoretical data and real field seismic data show that the proposed interpolation schemes can not only get the expected point's value, but also get a great accuracy in reconstruction of the seismic profile, leading to a significant improvement over other trace interpolation methods.

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