Theoretical aspects of aerospace image processing in quasi two-dimensional spectral space

• Published in: MATEC Web of Conferences Vol. 75; p. 3006
• Main Authors: Kostrov, B.V., Grigorenko, D.V., Ruchkin, V.N., Fulin, V.A.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Les Ulis EDP Sciences 01.01.2016
• Subjects: Correlation analysis; Digital imaging; Image processing; Mathematical analysis; Matrix methods; Theorems
• ISSN: 2261-236X; 2274-7214; 2261-236X
• DOI: 10.1051/matecconf/20167503006

The article regards digital images as mathematical objects and uses a co-variation matrix of element brightness values to analyze an autocorrelation matrix of images – a dispersion matrix, to define all significant properties of images with the help of mathematical statistics and matrix computing. We suggest theoretic and methodological generalizations in the field of aerospace photo processing, basing on choice of the most advantageous variant of constructing basic functions among various Vilenkin-Chrestenson functions (VCF) in a non-trigonometrical minimally available construction form as Walsh functions with an original ‘carcass’ of Rademacher functions. The methodology of this research is based on a set of theorems that are different from corresponding theorems of classical spectral analysis [5]. The conclusions of the theorems allow constructing effective algorithms of filtration and correlation analysis of aerospace images when noises and distortions appear.