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Quantization of KLT matrices using a GMRF model for image blocks with application to adaptive transform coding.

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Title: Quantization of KLT matrices using a GMRF model for image blocks with application to adaptive transform coding.
Authors: Boragolla, Rashmi1 (AUTHOR) borbnwmr@myumanitoba.ca, Yahampath, Pradeepa1 (AUTHOR) Pradeepa.Yahampath@umanitoba.ca
Source: EURASIP Journal on Image & Video Processing. 1/8/2026, Vol. 2026 Issue 1, p1-28. 28p.
Subjects: Gaussian Markov random fields, Vector quantization, Signal quantization, Mathematical transformations, Image compression
Abstract: Forward adaptive transform coding of images requires a codebook of transform matrices from which the best transform can be chosen for each macroblock. Codebook construction is a problem of designing a quantizer for Karhunen–Lóeve transform (KLT) matrices estimated from sample image blocks. We present a novel method for KLT matrix quantization based on a finite-lattice non-causal homogeneous Gauss–Markov random field (GMRF) model with asymmetric Neumann boundary conditions for blocks in natural images. The matrix quantization problem is solved in the GMRF parameter space, simplifying the harder problem of quantizing a large matrix subject to an orthonormality constraint to a low-dimensional vector quantization problem. Typically used GMRF parameter estimation methods such as maximum-likelihood (ML) do not necessarily maximize the coding performance of the resulting transform matrices. To this end we propose a method for GMRF parameter estimation from sample image data, which maximizes the high-rate transform coding gain. We also investigate the application of GMRF-based transforms to variable block-size adaptive transform coding. [ABSTRACT FROM AUTHOR]
Copyright of EURASIP Journal on Image & Video Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Quantization of KLT matrices using a GMRF model for image blocks with application to adaptive transform coding.
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  Data: <searchLink fieldCode="DE" term="%22Gaussian+Markov+random+fields%22">Gaussian Markov random fields</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+quantization%22">Vector quantization</searchLink><br /><searchLink fieldCode="DE" term="%22Signal+quantization%22">Signal quantization</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Image+compression%22">Image compression</searchLink>
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  Data: Forward adaptive transform coding of images requires a codebook of transform matrices from which the best transform can be chosen for each macroblock. Codebook construction is a problem of designing a quantizer for Karhunen–Lóeve transform (KLT) matrices estimated from sample image blocks. We present a novel method for KLT matrix quantization based on a finite-lattice non-causal homogeneous Gauss–Markov random field (GMRF) model with asymmetric Neumann boundary conditions for blocks in natural images. The matrix quantization problem is solved in the GMRF parameter space, simplifying the harder problem of quantizing a large matrix subject to an orthonormality constraint to a low-dimensional vector quantization problem. Typically used GMRF parameter estimation methods such as maximum-likelihood (ML) do not necessarily maximize the coding performance of the resulting transform matrices. To this end we propose a method for GMRF parameter estimation from sample image data, which maximizes the high-rate transform coding gain. We also investigate the application of GMRF-based transforms to variable block-size adaptive transform coding. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of EURASIP Journal on Image & Video Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Signal quantization
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              Text: 1/8/2026
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