The Lorentzian of Gaussian wavelet plotted in terms of its scale parameter a and position parameter b.
Peak identification of data (top, black) consisting of strongly overlapping Lorentzian peaks (top, dashed). The LoG wavelet transform at four scale parameters (bottom) is shown along with the local maxima and ridges, as defined in Sec. III B.
The analysis of the diffraction pattern of PtZn nanoparticles. Top: The diffraction pattern, the locations of the peaks identified by the wavelet-based algorithm (long lines), and the peak locations of PtZn from JCPDS card 03-066-0026 (short lines) (Ref. 12). Top-middle: The wavelet transform at wavelet scale 0.42 deg and the local maxima above the noise threshold (stars). Bottom-middle: The wavelet transform at 12 wavelet scales is shown for the entire wavelet position range. The local maxima above the noise threshold are shown as overlaid circles which are colored in grayscale according to the relative wavelet transform intensity within the respective ridge. Mother-descendant relations between ridges are shown by black lines connecting the local maxima. Bottom: The background-subtracted diffraction pattern and fitted peak profile (dashed).
An interpolated diffraction map of the Pt–Ru composition spread thin film. The measurement compositions are indicated by arrows on the left ordinate axis and the identified peaks at these compositions are plotted as stars.
The analysis of the diffraction pattern from the Pt–Ru thin film at 42 at. % Pt. Top: The diffraction pattern and the locations of the peaks identified by the wavelet-based algorithm (vertical lines). Middle: The wavelet transform at 23 wavelet scales is shown with overlaid ridges (see Fig. 3 for other notation). Bottom: A subset of the background-subtracted diffraction pattern and five fitted peaks (dashed).
The LoG wavelet transform of strongly overlapping Gaussian (top) and Lorentzian (bottom) peaks. The sum of the overlapping peaks is shown (black line) with its wavelet transform (right axis) at scale parameter a = 0.25. The plots (dotted lines) and functions of the constituent peaks are also shown.
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