Denoising algorithm

Roy M, Kumar V, Kulkami B, Sanderson J, Rodes M, van der Stappen M. Simple denoising algorithm using wavelet transform. AlChE J 45 2461 2466, 1999. 

Yang, K., Han, X. (2011) Accurate quantification of lipid species by electrospray ionization mass spectrometry - Meets a key challenge in lipidomics. Metabolites 1,21-40. Satten, G.A., Datta, S., Moura, H., Woolfitt, A.R., Carvalho Mda, G., Carlone, G.M., De, B.K., Pavlopoulos, A., Barr, J.R. (2004) Standardization and denoising algorithms for mass spectra to classify whole-organism bacterial specimens. Bioinformatics 20, 3128-3136. 

To implement the reconstruction of the initial image, using denoised and/or noisy data given by simulated projections The algorithm (1) and the Gibbs functional in the form (12) were used for the reconstruction. The coefficients a and P were optimized every time. 

Having a closer look at the pyramid algorithm in Fig. 40.43, we observe that it sequentially analyses the approximation coefficients. When we do analyze the detail coefficients in the same way as the approximations, a second branch of decompositions is opened. This generalization of the discrete wavelet transform is called the wavelet packet transform (WPT). Further explanation of the wavelet packet transform and its comparison with the DWT can be found in [19] and [21]. The final results of the DWT applied on the 16 data points are presented in Fig. 40.44. The difference with the FT is very well demonstrated in Fig. 40.45 where we see that wavelet describes the locally fast fluctuations in the signal and wavelet a the slow fluctuations. An obvious application of WT is to denoise spectra. By replacing specific WT coefficients by zero, we can selectively remove... 

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. 

Andreev VP, et al. A uiversal denoising and peak picking algorithm for LC-MS based on matched filtration in the chromatographic time domain. Anal Chem 2003 75 6314-6326. 

Andreev, V.P., Rejtar, T., Chen, H.S., Moskovets, E.V., Ivanov, A.R., Karger, B.L. (2003) A universal denoising and peak picking algorithm for LC-MS based on matched filtration in the chromatographic time domain. Anal. Chem. 75, 6314-6326. 

Adapted waveform analysis offers an even sharper means to divide signals into portions likely to be noise and portions likely to be non-noise. The ultimate form of this algorithm is matching pursuit, which uses huge families of waveforms and gives up computational speed in exchange for denoising efficiency. ... 

The rest of the paper is oiganized as follows in section 2, we described the basie eoncepts of measuring noise and details of the proposed algorithm, hr section 3, the results of the proposed method for denoising are shown and compared to other methods and finally in section 4, we presented our conclusions. 

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