Enhancement of Fractal Signal Using Constrained Minimization in Wavelet Domain

Yoshikazu MIYANAGA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A    No.6    pp.958-964
Publication Date: 1997/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing Theories and Applications Based on Modelling of Nonstationary Processes)
fractal signal,  signal reconstruction,  1/f process,  constrained optimization,  wavelet,  nonstationary process,  

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In recent years, fractal processes have played important roles in various application fields. Since a 1/f process possesses the statistical self-similarity, it is considered sa a main part of fractal signal modeling. On the other hand, noise reduction is often needed in real-world 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.