TRANSLATION-INVARIANT BASED ADAPTIVE THRESHOLD DENOISING FOR IMPACT SIGNAL

A translation-invariant based adaptive threshold denoising method formechanical impact signal is proposed. Compared with traditional wavelet denoising methods, itsuppresses pseudo-Gibbs phenomena in the neighborhood of signal discontinuities. To remedy thedrawbacks of conventional threshold functions, a new improved threshold function is introduced. Itpossesses more advantages than others. Moreover, based on utilizing characteristics of signal, aadaptive threshold selection procedure for impact signal is proposed. It is data-driven andlevel-dependent, therefore, it is more rational than other threshold estimation methods. Theproposed method is compared to alternative existing methods, and its superiority is revealed bysimulation and real data examples.

Translation-invariant wavelet denoising of full-tensor gravity-gradiometer data

Denoising of full-tensor gravity-gradiometer data involves detailed information from field sources, especially the data mixed with high-frequency random noise. We present a denoising method based on the translation-invariant wavelet with mixed thresholding and adaptive threshold to remove the random noise and retain the data details. The novel mixed thresholding approach is devised to filter the random noise based on the energy distribution of the wavelet coefficients corresponding to the signal and random noise. The translation- invariant wavelet suppresses pseudo-Gibbs phenomena, and the mixed thresholding better separates the wavelet coefficients than traditional thresholding. Adaptive Bayesian threshold is used to process the wavelet coefficients according to the specific characteristics of the wavelet coefficients at each decomposition scale. A two-dimensional discrete wavelet transform is used to denoise gridded data for better computational efficiency. The results of denoising model and real data suggest that compared with Gaussian regional filter, the proposed method suppresses the white Gaussian noise and preserves the high-frequency information in gravity-gradiometer data. Satisfactory denoising is achieved with the translation-invariant wavelet.

A GENERALIZATION OF LEBESGUE DIFFERENTIAL THEOREM AND ITS APPLICATION

The author generalizes the classical Lebesgue differential theorem to the case of rather general metrics. Then. the author applies it to the subelliptic metric to check the integral characterization of Holder continuous functions related to the metric.

Method and application of wavelet shrinkage denoising based on genetic algorithm

Genetic algorithm (GA) based on wavelet transform threshold shrinkage (WTS) and translation-invariant threshold shrinkage (TIS) is introduced into the method of noise reduction, where parameters used in WTS and TIS, such as wavelet function, decomposition levels, hard or soft threshold and threshold can be selected automatically. This paper ends by comparing two noise reduction methods on the basis of their denoising performances, computation time, etc. The effectiveness of these methods in-troduced in this paper is validated by the results of analysis of the simulated and real signals.

Invariance of shift-invariant spaces

In this paper, we give a characterization of shift-invariant subspaces which are also invariant under additional non-integer translations. Both principal and finitely generated shift-invariant subspaces are studied. Our results improve some known ones.