IMAGE PROCESSING BY KRAVCHUK POLYNOMIALS: OPEN QUESTION
DOI:
https://doi.org/10.31471/2304-7399-2025-21(79)-126-133Keywords:
Fourier series; orthogonal polynomials; Kravchuk polynomials; harmonic analysis; spectral methods; technical diagnostics; digital signal processing.Abstract
The study focuses on constructing spectral models of functions based on classical orthogonal polynomials, particularly Kravchuk polynomials, which serve as discrete analogs of continuous orthogonal bases. The use of such bases increases computational stability and speed, reduces approximation errors, and ensures the analytical representation of diagnostic signals in digital form. Discrete-variable bases are shown to be the most suitable for the development of software in non-destructive testing and diagnostic systems, as they eliminate the need for complex numerical integration. Special attention is paid to the analytical properties of Kravchuk polynomials, their recurrence relations, and their potential application in spectral transformations of functions. The problem of applying Kravchuk polynomials of several variables for image/speeach processing is formulated.
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