New Orthogonal Transforms for Signal and Image Processing
Abstract
:1. Introduction
2. Orthogonal Generalized Transform Matrix
- .
- .
- —transpose matrix I—unit matrix.
- —inverse matrix.
- C—coefficients .
- —positive real number.
3. Exponential Form of the Transform Matrix
- a—any real number, .
- k—integer, .
- .
- , —the elements of basis sequences for matrices and , respectively.
4. Signal Approximation—Orthogonal Expansion
5. Proposed Orthogonal Transform and Its Modifications
5.1. One-Dimensional (1D) Transform
- —vector of spectral components.
- —vector of 1D signal.
- —transform matrix defined by Equation (15).
- C—constant defined by Equation (16).
5.2. Two-Dimensional (2D) Transform
- —matrix of spectral components.
- —matrix of 2D signal.
- —transform matrix described by Equation (15).
- C—constant described by Equation (16).
6. Fast Algorithms
7. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Dziech, A. New Orthogonal Transforms for Signal and Image Processing. Appl. Sci. 2021, 11, 7433. https://doi.org/10.3390/app11167433
Dziech A. New Orthogonal Transforms for Signal and Image Processing. Applied Sciences. 2021; 11(16):7433. https://doi.org/10.3390/app11167433
Chicago/Turabian StyleDziech, Andrzej. 2021. "New Orthogonal Transforms for Signal and Image Processing" Applied Sciences 11, no. 16: 7433. https://doi.org/10.3390/app11167433
APA StyleDziech, A. (2021). New Orthogonal Transforms for Signal and Image Processing. Applied Sciences, 11(16), 7433. https://doi.org/10.3390/app11167433