GBST: Separable transforms based on line graphs for predictive video coding

Egilmez, Hilmi E.; Chao, Yung‐Hsuan; Ortega, Antonio; Lee, Bumshik; Yea, Sehoon

doi:10.1109/icip.2016.7532784

Cited by 22 publications

(31 citation statements)

References 14 publications

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“…Table IV shows that the proposed GSI significantly outperforms CGL for β > 0, and the average RE difference increases as β gets larger. This is because the variance shifting GBF leads to the noisy signal model with the covariance in (11) where β represents the variance of the noise (σ 2 ), and the prefiltering step allows GSI to perfectly estimate the parameter β from Σ by using (25) so that the covariance is prefiltered as in (15) based on the optimal β. The prefiltering step can also be considered as a denoising operation (reversing the effect of variance shifting GBFs) on the signal covariance before the graph estimation step, while CGL works with noisy (i.e., shifted) covariances, which diminish the CGL estimation performance.…”

Section: B Graph Learning From Variance/frequency Shifted Signalsmentioning

confidence: 99%

Graph Learning From Filtered Signals: Graph System and Diffusion Kernel Identification

Egilmez

Pavéz

Ortega

2019

IEEE Trans. on Signal and Inf. Process. over Networks

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This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter (a function of graph Laplacian matrices). In order to solve the proposed problem, an algorithm is developed to jointly identify a graph and a graph-based filter (GBF) from multiple signal/data observations. Our algorithm is valid under the assumption that GBFs are one-to-one functions. The proposed approach can be applied to learn diffusion (heat) kernels, which are popular in various fields for modeling diffusion processes. In addition, for specific choices of graph-based filters, the proposed problem reduces to a graph Laplacian estimation problem. Our experimental results demonstrate that the proposed algorithm outperforms the current state-of-the-art methods. We also implement our framework on a real climate dataset for modeling of temperature signals.

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Section: B Graph Learning From Variance/frequency Shifted Signalsmentioning

confidence: 99%

Graph Learning From Filtered Signals: Graph System and Diffusion Kernel Identification

Egilmez

Pavéz

Ortega

2019

IEEE Trans. on Signal and Inf. Process. over Networks

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“…For modeling video block signals, we use Gaussian Markov random fields (GMRFs), which provide a probabilistic interpretation for our graph-based framework. Assuming that the random vector of interest x ∈ R n has zero mean 2 , a GMRF 2 The zero mean assumption is made to simplify the notation. The models can be trivially extended to GMRFs with nonzero mean.…”

Section: Graph-based Models and Transforms For Video Block Signalsmentioning

confidence: 99%

“…In our previous work [2], we introduced the 1-D GMRFs illustrated in Fig. 2 for intra/inter predicted signals and also derived closed-form expressions of their precision matrices (i.e., Ω).…”

Section: Propositionmentioning

confidence: 99%

“…On the other hand, for the transformation, generally a single transform such as the H.E. Egilmez [1], [2] and in the PhD dissertations [3], [4]. discrete cosine transform (DCT-2) is applied in a separable manner to rows and columns of each residual block.…”

Section: Introductionmentioning

confidence: 99%

“…• We propose graph learning techniques for separable and nonseparable GBTs, i.e., GBSTs and GBNTs, respectively, and present a theoretical justification of their use for coding residual block signals modeled using GMRFs. • As an extension of the 1-D GMRF models used to design GBSTs for intra and inter predicted signals in our previous work [2], we present a general 2-D GMRF model for GBNTs and analyze its optimality. • We apply EA-GBTs to intra and inter predicted blocks, while our prior work in [1] focused only on inter predicted blocks.…”

Section: Introductionmentioning

confidence: 99%

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Graph-based transforms for inter predicted video coding

Egilmez

Said

Chao

et al. 2015

2015 IEEE International Conference on Image Processing (ICIP)

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In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes two different techniques to design GBTs. In the first technique, we formulate an optimization problem to learn graphs from data and provide solutions for optimal separable and nonseparable GBT designs, called GL-GBTs. The optimality of the proposed GL-GBTs is also theoretically analyzed based on Gaussian-Markov random field (GMRF) models for intra and inter predicted block signals. The second technique develops edge-adaptive GBTs (EA-GBTs) in order to flexibly adapt transforms to block signals with image edges (discontinuities). The advantages of EA-GBTs are both theoretically and empirically demonstrated. Our experimental results demonstrate that the proposed transforms can significantly outperform the traditional Karhunen-Loeve transform (KLT).

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Graph Spectral Image Processing

Cheung

Magli

Tanaka

et al. 2021

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GBST: Separable transforms based on line graphs for predictive video coding

Cited by 22 publications

References 14 publications

Graph Learning From Filtered Signals: Graph System and Diffusion Kernel Identification

Graph Learning From Filtered Signals: Graph System and Diffusion Kernel Identification

Graph-based transforms for inter predicted video coding

Graph Spectral Image Processing

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