The new mathematical method for processing is proposed. The method is based on factorization the source data in an orthogonal basis adapted to the standard mass-spectra data. Orthogonal transformations can be represented in the form of matrix equation Y = HX (1), where X — initial vector of source data, H — operator of the orthogonal transformation, Y — vector of data after factorization. Theoretical justification of such transformations has been developed in works made by prof. Alexey Solodovnikov and his successors [1]. The system of adapted basis functions can be build on the base of a standard R_st. An operator of orthogonal transform H is considered to be adapted if the one meets the condition: H R_st = Y_t = [y_t1,0,...,0] (2), Y_t — target vector, taken as operator adjustment criterion, R_st = [r_st,1,...,r_st,N] — the vector of standard mass spectrum. Standard mass spectrum is ideal mass spectrum of the pure product without noise, without contaminations and with peaks of well known shape. Standard mass spectrum (line 1), standard mass spectrum with contaminations (line 2) and mass spectrum of contaminations (line 3) are shown on the Fig.1. In Fig.1 the axis of abscissas is mass.

The presentation of factorization of standard mass-spectrum in adapted basis function according to equation (2) is shown in Fig. 2. The presentation of the factorization of the standard mass spectrum with contaminations in adapted basis function according to equation (1) is shown in Fig 3. In the Fig. 2 and Fig.3 the axis of abscissas is spectral coefficient k.

One can distinguish pure mass spectrum from mass spectrum with contaminations by comparing the transformed signals according to equation (1). Those comparison can be done by testing the inequalities

(3)

Y — vector of source data transformed according to equation (1) Y_st — vector of standard data transformed according to equation (2). Y – Y_st — norm of difference of two vectors. Y(1), Y_st(1) — elements of vectors for spectral coefficient k = 1. If inequalities (3) are true, then our source data are pure mass spectrum, else mass spectrum has contaminations. Parameters δ and ε are chosen in learning process considering the shape of peaks and the variance of the noise.

Main advantages of proposed method consist in the independence from shape of mass spectrum peak, in simplicity of achievement, and possibility to detect multiplets in mass spectrum data.

References:
1. Solodovnikov. A.I. Spivacovsky А.М. Fundamentals of theory and methods of spectral processing information. School-book Publisher Leningrad University, 1986. 272 pages (in russian)