Using Adaptive Window Wavelet Neural Network to Solve a Spectroscopy Inverse Problem
Working with real measurement data to solve inverse problems of classification and regression requires elimination of noise components for the correct solution of the problem. In the widely used signal processing approach, Fast Fourier Transform  is used to eliminate high frequency and low frequency components of signal. The main problem of this approach is that real observations may contain useful information in high and low frequency domains simultaneously, but with different localization in the signal. For example, Raman spectra of inorganic salts have sharp peaks in the low frequency part of the spectra, and a smooth water valence band in the high frequency part of spectra, also changing its shape depending on the dissolved substances and their concentrations .
One of the widely used (especially in EEG processing ) methods of signal processing considering different localization of different frequencies is Wavelet transformation . Wavelet transformation uses a special basis widely known for its unique properties, the most important of which are its compactness and multiresolution (wavelet functions are produced from the mother wavelet by transition and dilation).
Wavelet neural networks (WNN)  use wavelet functions to decompose the approximated function. However, for a standard wavelet basis with fixed transition and dilation coefficients, the decomposition may be not optimal. If no inverse transformation is needed, the values of transition and dilation coefficients may be determined during network training, and the windows corresponding to various wavelet functions may overlap.
In this study, we suggest a new type of a WNN—Adaptive Window WNN (AWWNN) , designed primarily for signal processing, in which window positions and wavelet levels are determined with a special iterative procedure. Two modifications of this new type of WNN are tested against a linear model and a multi-layer perceptron. The developed network was used to solve the inverse problem of Raman spectroscopy on determination of the concentrations of 10 inorganic salts, dissolved in water. A more detailed description of the measurements and of sample preprocessing is presented in the paper . The AWWNN demonstrated promising results with mean absolute error less than that of a classical multilayer dense neural network.
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D.V.Skobeltsyn Institute of Nuclear Physics, M.V.Lomonosov Moscow State University, Moscow 119991, Russia
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