The Properties and Application of the Cosine Transform Subband Matrices

Evgeniy G. Zhilyakov, Andrey A. Chernomorets, Evgeniya V. Bolgova, Mariya A. Petina and Anastasiya N. Kovalenko

We study the properties of the subband cosine transform matrices used for solving the image processing tasks in this paper. The construction of subband matrices is based on the image frequency representation which uses the cosine transform. Based on the Parseval’s equation for representing of the image energy part in a given subdomain of the cosine transform definition domain, the formulas are obtained for calculating of the subband matrices elements values. It is shown that these matrices are representable as the sum of the known subband matrices based on the Fourier transform (in exponential form) and the so-called quasi-subband matrices. The study of the quasi-subband matrices properties is carried out. It is shown that they are Hankel, symmetric, real matrices. The analysis of their eigenvalues and eigenvectors properties is carried out. We also study the properties of subband matrices in this paper. It is shown that they are symmetric, real matrices, their eigenvalues are non-negative. It is shown that the energy part value of a subband matrix eigenvector in the frequency subdomain for which this matrix is constructed coincides with the corresponding eigenvalue. In the paper we present the formula based on subband matrices for the image filtering (highlighting the individual components) in a given frequency sub-domain of the cosine transform. An example of using subband matrices for image filtering in a given frequency subdomain is given in the paper.

Volume 12 | 05-Special Issue

Pages: 1302-1313

DOI: 10.5373/JARDCS/V12SP5/20201890