Extensions of Fractional Brownian Fields and Morphological Spectral Analysis for Discrimination of Catalysts

Abstract : The thesis concerns statistical characterization of spatial arrangements of fringes (active phases) in the catalysts imaged by High Resolution Transmission Electron Microscopy (HRTEM). The contributions proposed in this thesis are two statistical models for the description of these HRTEM image contents. The first model involves 2-D Fractional Brownian Field (FBF) and 2-D Auto Regressive (AR) models, as well as morphological analysis of the spectra associated with these models (ARFBF morphological analysis). Concerning FBF modeling, we propose two methods for estimating its parameter: Log-RDWP (Log-Regression on Diagonal Wavelet Packet spectrum) and Log-RPWP (Log-Regression on Polar representation of Wavelet Packet spectrum). We propose a morphological method on ARFBF spectrum for detecting and identifying HRTEM texture features. It is shown that the morphological properties of spectral features make possible, a separation between different catalysts. The second model proposed in this thesis is a generalization of FBF (GFBF) constructed by using convolution and modulation operators of several FBF. The textures synthesized from GFBF model are shown to present some structural similarities with certain fringe structures present in HRTEM images. We details association of a GFBF to an HRTEM fringe by considering a GFBF mixture comprising an FBF and a modulated version of FBF (model called CMFBF). This CMFBF has a spectral representation associated with two poles (spectral peaks) and two Hurst parameters. The spectral peak at zero frequency characterizes the background of the HRTEM image and the first Hurst parameter describes the regularity of this background. The second peak and its corresponding Hurst parameter is representative of the fringe structural and spectral contents.
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Zhangyun Tan. Extensions of Fractional Brownian Fields and Morphological Spectral Analysis for Discrimination of Catalysts. Methodology [stat.ME]. Université Grenoble Alpes, 2016. English. ⟨tel-01532841⟩

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