Scaling and correlation analysis of galactic images
P. Frick, R. Beck, E. M. Berkhuijsen, I. Patrickeyev · 2001
Different scaling and autocorrelation characteristics and their application to astronomical images are discussed: the structure function, the autocorrelation function, Fourier spectra and wavelet spectra. The choice of the mathematical tool is of great importance for the scaling analysis of images. The structure function, for example, cannot resolve scales which are close to the dominating large-scale structures and can lead to the wrong interpretation that a continuous range of scales with a power law exists. The traditional Fourier technique, applied to real data, gives very spiky spectra, in which the separation of real maxima and high harmonics can be difficult. We recommend as the optimal tool the wavelet spectrum with a suitable choice of the analysing wavelet. We introduce the wavelet cross-correlation function which enables to study the correlation between images as a function of scale. The cross-correlation coefficient strongly depends on the scale. The classical cross-correlation coefficient can be misleading if a bright, extended central region or an extended disk exists in the galactic images.