Denoising and compression

Depezynski, U., Jetter, K., Molt, K and Niemoller, A. (1999b) The fast wavelet transform on compact intervals as a tool in chemometrics. II. Boundary effects, denoising and compression. Chemom. Intell. Lab. Syst., 49, 151—161. 

Denoising and compression of data with Gaussian errors... 

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. 

Up to December 1998, more than 30 publications have reported spectroscopic studies with the use of a WT algorithm [9,10], Within this work, WT has been utilized in three major areas that include data denoising, data compression, and pattern recognition. Two classes of wavelet algorithm namely discrete wavelet transform (DWT) and wavelet packet transform (WPT), have been commonly adopted in the computation. The former one is also known as the fast wavelet transform (FWT). The general theory on both FWT and WPT can be found in other Chapters of this book and some chemical journals [16-18], and is not repeated here. In the following sections, selected applications of WT in different spectral techniques will be described. 

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. 

All compression, denoising, and data reduction methods retain the largest Nx number of coefficients depending on the choice of appropriate threshold k. These methods follow the principle assuming that large wavelet coefficients characterize signal better in the sense of its energy and thus retain more information. 

J. Trygg, Wavelets in Chemometrics - Compression, Denoising, and Feature Extraction, 2003... 

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

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. 

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