Dynamic process analysis by moments of extreme orders

Dynamic processes in astronomical observations are captured in various video sequences. The image datacubes are represented by the datasets of random variables. Diagnostics of a fast developing event is based on the specific behavior of the high-order moments (HOM) in time. The moment curves computed in an image video sequence give valuable information about various phases of the phenomenon and significant periods in the frequency analysis. The proposed method uses statistical moments of high and very high orders to describe and investigate the dynamic process in progress. Since these moments are highly correlated, the method of principal component analysis (PCA) has been suggested for following frequency analysis. PCA can be used both for decorrelation of the moments and for determination of the number of used moments. We experimentally illustrate performance of the method on simulated data. A typical development of the dynamic phenomenon is modeled by the moment time curve. Then applications to the real data sequences follow: solar active regions observed in the spectral line Hαα (wavelength 6563 A˚—Ondřejov and Kanzelhöhe observatories) in two different angular resolutions. The frequency analysis of the first few principal components showed common periods or quasi-periods of all examined events and the periods specific for individual events. The detailed analysis of the moment’s methodology can contribute to the observational mode settings. The method can be applied to video sequences obtained by observing systems with various angular resolutions. It is robust to noise and it can work with high range of sampling frequencies.