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Article

New Orthogonal Transforms for Signal and Image Processing

Institute of Telecommunications, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
Academic Editor: Volodymyr Mosorov
Appl. Sci. 2021, 11(16), 7433; https://doi.org/10.3390/app11167433
Received: 9 July 2021 / Revised: 30 July 2021 / Accepted: 5 August 2021 / Published: 12 August 2021
(This article belongs to the Special Issue Novel Advances of Image and Signal Processing)
In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of the important features of the presented approach. The conditions for creating symmetric, orthogonal matrices are defined. It is shown that for the selection of the elements of an orthogonal matrix that meets the given conditions, it is necessary to select only a limited number of elements. The general form of the orthogonal, symmetric matrix having an exponential form is also presented. Orthogonal basis functions based on the created matrices can be used for orthogonal expansion leading to signal approximation. An exponential form of orthogonal, sparse matrices with variable parameters is also created. Various versions of orthogonal transforms related to the created full and sparse matrices are proposed. Fast computation of the presented transforms in comparison to fast algorithms of selected orthogonal transforms is discussed. Possible applications for signal approximation and examples of image spectrum in the considered transform domains are presented. View Full-Text
Keywords: orthogonal transform; signal processing; image processing orthogonal transform; signal processing; image processing
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MDPI and ACS Style

Dziech, A. New Orthogonal Transforms for Signal and Image Processing. Appl. Sci. 2021, 11, 7433. https://doi.org/10.3390/app11167433

AMA Style

Dziech A. New Orthogonal Transforms for Signal and Image Processing. Applied Sciences. 2021; 11(16):7433. https://doi.org/10.3390/app11167433

Chicago/Turabian Style

Dziech, Andrzej. 2021. "New Orthogonal Transforms for Signal and Image Processing" Applied Sciences 11, no. 16: 7433. https://doi.org/10.3390/app11167433

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