Denoising Smoothing

The method has many applications among them arc Denoising Smoothing (DS), compression, and Feature Extraction (FE), which arc powerful tools for data transformations. See the "Selected Reading" section at the end of this chapter for further details. 

Barclay, V.J., Bonner, R.F., and Hamilton, I.P., Application of wavelet transform to experimental spectra smoothing, denoising, and data set compression, Anal. Chem., 69, 78, 1997. 

V.J. Barclay, R.F. Bonner and I.P. Hamilton. Application of Wavelet Transforms to Experimental Spectra Smoothing, DENOISING, and Data Set Compression, Analytical Chemistry. 69 (1997), 78-90. 

Data compression is another application of WT that has shown remarkable results (Artursson and Holmberg 2002). The mathematical treatment for data compression by WT is similar to that for denoising and smoothing (fetter et al. 2000). Chemical data is treated with WT and transformed to the scale-time domain where its spectral content is reduced by elinunating coefficients belonging to high frequency content. Compression with this teclmique is highly efficient since a one level decomposition and... 

ABSTRACT This paper provides a short review of recent developments in crash pulse analysis methods and a short review of wavelet based data processing methods. A discrete wavelet transform can he performed in 0 n) operations, and it captures not only a frequency of the data, but also spatial informations. Moreover wavelet enables sparse representations of diverse types of data including those with discontinuities. And finally wavelet based compression, smoothing, denoising, and data reduction are performed by simple thresholding of wavelet coefficients. Combined, these properties make wavelets a very attractive tool in mary applications. Here, a noisy crash signals are analyzed, smoothed and denoised by means of the discrete wavelet transform. The optimal choice of wavelet is discussed and examples of crash pulse analysis are also given. 

Figure 13 WT-based smoothing has four steps (1) Transform the signal, (2) isolate the wavelet coefficients corresponding to the high-frequency components, (3) zero-out or reduce these coefficients, and (4) apply a reverse W T to the signal. Compare this with the denoising routine illustrated in Figure 14.

Transforms to Experimental Spectra Smoothing, Denoising, and Data Set Compression. 

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