Reference for citation: Sergeev А. M. Two-level and modularly two-level quasi-orthogonal Walsh-structured matrices for image masking. Journal of Instrument Engineering. 2023. Vol. 66, N 5. P. 399—408 (in Russian). DOI: 10.17586/0021-3454-2023-66-5-399-408.

Abstract. A separate class of quasi-orthogonal matrices, namely, two-level Mersenne matrices structured according to Walsh, are studied. The difference between the systems of orthogonal Hadamard–Walsh and Mersenne–Walsh functions is shown. Modular two-level Mersenne–Walsh matrices and their portraits are considered. A system of functions constructed using a modularly two-level Mersenne–Walsh matrix has twice as many levels as a system of functions constructed on the basis of a two-level Mersenne matrix structured according to Walsh. As an applied problem using structured quasi-orthogonal matrices, the procedure for masking images with two-level and modularly two-level Mersenne-Walsh matrices with an assessment of the results of masking - destruction of the original image is considered. The example of a test image demonstrates the change in the brightness histogram and the influence of the order of the masking matrix on the masking result.

Keywords: quasi-orthogonal matrices, Hadamard–Walsh matrices, Mersenne–Walsh matrices, modular two-level matrices, image masking

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