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1 October 2024 Exact short-length KLT for image processing and compression applications
Yuriy A. Reznik, Abhijith Jagannath
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Proceedings Volume 13137, Applications of Digital Image Processing XLVII; 1313712 (2024) https://doi.org/10.1117/12.3026800
Event: Optical Engineering + Applications, 2024, San Diego, California, United States
Abstract
Karhuen-Loeve Transform (KLT) is a valuable tool in many applications, but its computation is not exactly trivial. Generally, it requires finding the solution of an eigenvector problem, and with general types of inputs, the typical path forward is to use iterative numerical methods. Such methods are usually complex. In some cases, KLTs allow approximations by sinusoidal transforms – DCT-II likely the best-known example, but the number of such cases is limited, and usually constrained to very simple (1-st order) processes. However, as we will show in this paper, for some short sizes, KLTs can still be computed analytically, with only mild assumptions about the structure of the covariance matrix. For example, we show analytic solutions for arbitrary real symmetric 3x3 covariance matrixes. With symmetric 3-diagonal and some special cases of 5-diagonal matrices the solutions can also be found. In the end, we discuss a few possible applications of such transforms for image and video coding.
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(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.
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Yuriy A. Reznik and Abhijith Jagannath "Exact short-length KLT for image processing and compression applications", Proc. SPIE 13137, Applications of Digital Image Processing XLVII, 1313712 (1 October 2024); https://doi.org/10.1117/12.3026800
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KEYWORDS
Image compression
Image processing
Covariance matrices
Analytics
Covariance
Eigenvectors
Numerical analysis
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