Wavelet analysis of one- and two-dimensional data sets

Wavelet analysis allows considering one- and two-dimensional data sets at different resolution levels. The wavelet transform acts as a mathematical microscope providing a multiresolution analysis of data and disclosing structural features at different scales. The multiresolution decomposition of a data set gives finer scales approximation with a closer view of the data, whereas the coarse scale approximation reveals a "faraway view" of the data. The wavelet analysis will be used to one-dimensional data sets from the Raman spectroscopic investigations. It will be particularly important to be able to disclose small detailed changes in the Raman spectra from carbon nanotubes as they are subject to external loading. Similarly, X-ray reconstructed images (two-dimensional data sets) have been analized from multiresolution point of view in order to enhance details of microstructure, which are apparently not visible by a naked eye, enhancing borderlines, edges and removing noise. Quantitative analysis of microcellular microstructure will be performed in order to detect multiscale directionality of cell walls, which may result in anisotropic overall behaviour of these materials. (Ryszard Pyrz)