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Rovira i Virgili, CERTIFY: That the Doctoral thesis entitled: "VALIDATION OF QUALITATIVE ANALYTICAL METHODS", submitted by ESTHER TRULLOLS SOLER to obtain the degree of Doctor from the Universitat Rovira i Virgili, has been carried out under our supervision in the Analytical Chemistry Area of the Department of Analytical Chemistry and Organic Chemistry at the Universitat Rovira i Virgili, and all the results presented in this thesis were obtained in experiments conducted by the above mentioned student.

The wavelet transform was applied to Raman spectra to remove heteroscedastic noise from ancient pigments such as azurite and ultramarine blue. Wavelets from the Daubechies, Coiflet and Symmlet families were evaluated. Two different thresholding strategies on the detail coefficients were applied; the first is a one-dimensional variance adaptive thresholding and the second is a block threshold denoising. The block thresholding strategy removes the noise and preserves the band shapes best. Background removal during the denoising process was also investigated and the results were very good when the block thresholding strategy was used to suppress background at the optimal level of the denoising process. INTRODUCTIONToday, Raman spectroscopy is widely recognized as a powerful, non-destructive technique for characterizing materials. It is particularly well suited to identifying ancient pigments in cultural heritage studies 1 because it provides a 'fingerprint' of the material being analysed. Analysing spectra is often difficult because of the presence of noise and background signals. It is also difficult to apply chemometric techniques to this type of data 2,3 in the presence of nonstationary noise and a non-constant varying spectroscopic background.In Raman spectra from ancient pigments, the major contributor to background noise is the intrinsic fluorescence of the pigment components and binding materials. Considerable effort has been made to improve the spatial resolution of the technique so that small grains of pigment can be analysed with little or no interference from surrounding areas. However, pigment fluorescence is still present, and is usually several orders of magnitude more intense than the weak Raman scattering, so the spectrum is completely dominated by fluorescence. Another source of noise to be considered is the detector, as is the case when a charge-coupled device (CCD) detector is used. 4 In the study of pigments, however, Ł Correspondence to: Itziar Ruisánchez, Departament de Química Analítica i Química Orgànica, Universitat Rovira i Virgili, Campus Sescelades, C/. MarcelÐlí Domingo s/n, 43007 Tarragona, Spain. E-mail: itziar.ruisanchez@urv.net Contract/grant sponsor: European Community; Contract/grant number: G6RD-CT2001-00602. noise is usually more sample dependent than detector dependent. One important cause may be unspecific absorption or radiation by coloured or black samples.Noise removal is an important operation in data processing but today there is no general denoising strategy. Denoising strategies, including parameter selection, are strongly dependent on the problem involved. They depend on the signal-to-noise ratio, on the shape of the signals and their superposition, on the resolution of complex overlaid signals and on the justification or violation of model assumptions regarding noise distribution. Wavelet transform (WT) is a relatively new denoising technique which in recent years has been increasingly recognized for its relevance to analytical chemistry 5 and today it is a high-p...

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