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Using the orthogonal projection method to identify small objects in multispectral analysis

A.V. Gerus¹ , E.V. Savchenko¹ , V.P. Savorskiy^{1, 2}

¹ V. A. Kotelnikov Institute of Radioengineering and Electronics RAS, Fryazino Branch, Fryazino, Moscow region, Russia
² Space Research Institute RAS, Moscow, Russia

Accepted: 19.07.2018
DOI: 10.21046/2070-7401-2018-15-4-27-35

A method for recognizing small objects (less than the resolution of equipment) on a known background in a multispectral analysis is proposed. The method is based on four main principles. First, the normalized spectra are used rather than the initial ones, which leads to a significant variability reduction for all backgrounds studied. Second, a special calibration is employed, when all signal and background spectral components are normalized to their average values for the background with the corresponding weight coefficients. Third, a procedure is applied for calculating the modules of the orthogonal projection onto the normalized background and the spectrum vectors under study, which should have a minimum value for the correct hypothesis about the unknown signal. The fourth principle is statistical processing of the obtained results when spectra of those different points are taken into account where only the background is present. The results of identification of different objects by our method were compared with a known method based on the minimization of the standard deviation of the calculated value from the investigated one. 40 spectra of different background points were selected and four objects on airfield near Moscow were considered. For the background fraction in the mixture up to 85−95 %, the simulation showed a confident recognition of all four objects under consideration, which in almost all cases was much better than the results obtained by the mean square method.

Keywords: orthogonal projection, variability, extended multidimensional space

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