Smoothing methods wavelet transforms

X.Q. Lu and J.Y. Mo, Methods of Handling Discrete Data for Deconvolution Voltammetry (I) Wavelet Transform Smoothing, Chemical Journal of Chinese University, 18 (1997), 49-51 (in Chinese). 

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. 

Traditional transforms like the wavelet transform provide efficient representations for smooth images but suffer from curve discontinuities. Therefore, it is desirable to have a compression method that provides efficient representation of edges by exhibiting singularities along arbitrarily shaped curves, which may lead to improvements in compression performance. The compression procedure using the ripplet transform is formulated as follows [22] ... 

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