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Enhancement of Fractal Signal Using Constrained Minimization in Wavelet Domain
Jun'ya SHIMIZU Yoshikazu MIYANAGA Koji TOCHINAI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E80A
No.6
pp.958964 Publication Date: 1997/06/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Signal Processing Theories and Applications Based on Modelling of Nonstationary Processes) Category: Keyword: fractal signal, signal reconstruction, 1/f process, constrained optimization, wavelet, nonstationary process,
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Summary:
In recent years, fractal processes have played important roles in various application fields. Since a 1/f process possesses the statistical selfsimilarity, it is considered sa a main part of fractal signal modeling. On the other hand, noise reduction is often needed in realworld signal processing. Hence, we propose an enhancement algorithm for 1/f signal disturbed by white noise. The algorithm is based on constrained minimization in a wavelet domain: the power of 1/f signal distortion in the wavelet domain is minimized under a constraint that the power of residual noise in the wavelet domain is smaller than a threshold level. We solve this constrained minimization problem using a Lagrangian equation. We also consider a setting method of the Lagrange multiplier in the proposed algorithm. In addition, we will confirm that the proposed algorithm with this Lagrange multiplier setting method obtains better enhancement results than the conventional algorithm through computer simulations.

