A Novel Algorithm of the Wavelet Packets Transform and its Application to DE-Noising of Analytical Signals

ABSTRACT A novel algorithm of the wavelet packets transform, which is more suitable than the multiresolution signal decomposition (MRSD) algorithm to process the practical signals in analytical instrumental analysis, was proposed. There is no limitation of data length for the algorithm like the MRSD algorithm and, sometimes, no need to perform the inverse transform in practical uses by the algorithm. Two methods for de-noising were proposed based on the algorithm, and application of the methods to de-noising of noisy chromatograms was investigated. The results showed that the efficiency of the proposed methods is higher than that of the conventional thresholding methods.

[1]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[2]  Manfred Grasserbauer,et al.  Detection and Estimation of Heteroscedastic Noise by Means of the Wavelet Transform , 1997 .

[3]  Sg Nikolov,et al.  Improvement of SIMS image classification by means of wavelet de-noising , 1997 .

[4]  Douglas B. Kell,et al.  Wavelet Denoising of Infrared Spectra , 1997 .

[5]  Emmanuel Bacry,et al.  Wavelet based fractal analysis of DNA sequences , 1996 .

[6]  M. Wolkenstein,et al.  Wavelet filtering for analytical data , 1997 .

[7]  M.L. Hilton,et al.  Wavelet and wavelet packet compression of electrocardiograms , 1997, IEEE Transactions on Biomedical Engineering.

[8]  M. Bos,et al.  Wavelet transform for the evaluation of peak intensities in flow-injection analysis , 1992 .

[9]  Junbin Gao,et al.  Application of the Fast Wavelet Transform Method to Compress Ultraviolet-Visible Spectra , 1996 .

[10]  D. Massart,et al.  Application of wavelet transform to extract the relevant component from spectral data for multivariate calibration. , 1997, Analytical chemistry.

[11]  Guiwen Zhao,et al.  Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform , 1998 .

[12]  R. Bonner,et al.  Application of wavelet transforms to experimental spectra : Smoothing, denoising, and data set compression , 1997 .

[13]  D. Kell,et al.  An introduction to wavelet transforms for chemometricians: A time-frequency approach , 1997 .

[14]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Desire L. Massart,et al.  Noise suppression and signal compression using the wavelet packet transform , 1997 .

[16]  M. Bos,et al.  The wavelet transform for pre-processing IR spectra in the identification of mono- and di-substituted benzenes , 1994 .

[17]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[18]  Xiaoyong Zou,et al.  Spline wavelet multifiltering analysis , 1997 .

[19]  Desire L. Massart,et al.  Standardization of near-infrared spectra in the wavelet domain , 1997 .

[20]  Sg Nikolov,et al.  DE-NOISING OF SIMS IMAGES VIA WAVELET SHRINKAGE , 1996 .

[21]  X. Shao,et al.  Quantitative determination of the components in overlapping chromatographic peaks using wavelet transform. , 1997, Analytical chemistry.

[22]  Hong-Yuan Chen,et al.  Wavelet analyses of electroanalytical chemistry responses and an adaptive wavelet filter , 1997 .

[23]  M. Grasserbauer,et al.  Wavelet denoising of Gaussian peaks: A comparative study , 1996 .

[24]  Jean-Marie Dereppe,et al.  The continuous wavelet transform, an analysis tool for NMR spectroscopy , 1997 .

[25]  Junbin Gao,et al.  Compression of Infrared Spectral Data Using the Fast Wavelet Transform Method , 1997 .