NOISE FILTERING OF MULTISPECTRAL DIGITAL SIGNALS: OPTIMIZATION APPROACH

Abstract

The article proposes a method of filtering additive noise on digital raster images obtained in an arbitrary number of spectral intervals of radiation – the carrier of species information. The method is based on compression of image brightness codes, optimized according to two criteria: 1) minimization of the relative information entropy of the compressed image relative атв the primary (directly fixed) image; 2) maximizing the ratio of the signal energy of the informative signal stored in the compressed image to the signal interference energy (signal-to- noise ratio). The implementation of the proposed method includes the following steps: representation of a set of images of spectral bands by a single multidimensional geometric object (MGO) in the form of a data array, ordered by raster and spectral intervals; Peano-Hilbert reamer of MGO with obtaining a one-dimensional digital signal; compression of reamer values according to the specified criteria; reconstruction of brightness codes of compressed images of spectral bands by functional transformation inverse to that used by compression. Noise filtering with simultaneous compression of digital brightness codes of images is implemented on the basis of decompositions of these codes on discrete orthonormalized functional bases, zeroing the part of the decomposition coefficients and subsequent reconstruction of image brightness distributions. Determination of thresholds for zeroing coefficients of schedules of digital brightness levels is formulated in the form of a two-criteria optimization problem of minimizing the deviations of the relative information entropy of the compressed image with respect to the original image and the signal-to- noise ratio in the compressed image from predetermined values. The proposed method provides a compromise between the requirements of increasing the signal-to- noise ratio and preserving the informativeness of the synthesized images in relation to the primary species data. Comparison of different discretized functional bases as the basis for compression of brightness distributions showed the greatest efficiency according to the specified criteria of the Hartley basis.