Efficient Rate-distortion Approximation and Transform Type Selection using Laplacian Operators

Lu, Keng-Shih; Ortega, Antonio; Mukherjee, Debargha; Chen, Yue

doi:10.1109/pcs.2018.8456313

Cited by 8 publications

(9 citation statements)

References 19 publications

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“…Namely, there are 16 2D transforms candidates, (T col , Trow) with T col , Trow ∈ {U, V, JV, I}, which makes the encoder computationally expensive. Recent work on encoder complexity reduction includes [23], [57], [58], which apply heuristic and datadriven techniques to prune transform types during the search.…”

Section: B Transform Type Selection In Video Codingmentioning

confidence: 99%

“…Extending our previous experiment PRUNE LAPLACIAN in [23], we implemented a new experiment named PRUNE OPERATORS in AV1 5 . We implement the integer versions of the transform cost evaluation (29) for transform lengths 4, 8, 16, and 32.…”

Section: B Transform Type Selection In Video Codingmentioning

confidence: 99%

“…. , Z (m) } that are jointly diagonalizable (i.e., have a common eigenbasis) can be obtained for both cycle graphs [22] and line graphs [23]. Essentially, those operators are by themselves graph filter matrices with different frequency responses.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to filter operation, our approach can also be used to evaluate the transform domain weighted energy given by the Laplacian quadratic form, which has been used for ratedistortion optimization in the context of image and video coding [34], [35]. Following our recent work [23], we implement the proposed method in AV1, a real-world codec, where our method provides a speedup in the transform type search procedure.…”

Section: Introductionmentioning

confidence: 99%

“…Our work complements the study in [24] by considering 1) the case where GFT is a DTT, which corresponds to various line graphs, and 2) techniques to design MPGFs. In addition, the work presented in this paper is a more general framework than our prior work in [23], since the Laplacian quadratic form operation used in [23] can be viewed as a special case of graph filtering operation. Furthermore, while our work in [23] was restricted to DCT/ADST, in this paper we have extended these ideas to all DTTs.…”

Section: Introductionmentioning

confidence: 99%

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DCT and DST Filtering with Sparse Graph Operators

Lu,

Ortega,

Mukherjee

et al. 2021

Preprint

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Graph filtering is a fundamental tool in graph signal processing. Polynomial graph filters (PGFs), defined as polynomials of a fundamental graph operator, can be implemented in the vertex domain, and usually have a lower complexity than frequency domain filter implementations. In this paper, we focus on the design of filters for graphs with graph Fourier transform (GFT) corresponding to a discrete trigonometric transform (DTT), i.e., one of 8 types of discrete cosine transforms (DCT) and 8 discrete sine transforms (DST). In this case, we show that multiple sparse graph operators can be identified, which allows us to propose a generalization of PGF design: multivariate polynomial graph filter (MPGF). First, for the widely used DCT-II (type-2 DCT), we characterize a set of sparse graph operators that share the DCT-II matrix as their common eigenvector matrix. This set contains the well-known connected line graph. These sparse operators can be viewed as graph filters operating in the DCT domain, which allows us to approximate any DCT graph filter by a MPGF, leading to a design with more degrees of freedom than the conventional PGF approach. Then, we extend those results to all of the 16 DTTs as well as their 2D versions, and show how their associated sets of multiple graph operators can be determined. We demonstrate experimentally that ideal low-pass and exponential DCT/DST filters can be approximated with higher accuracy with similar runtime complexity. Finally, we apply our method to transform-type selection in a video codec, AV1, where we demonstrate significant encoding time savings, with a negligible compression loss.

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Section: B Transform Type Selection In Video Codingmentioning

confidence: 99%

Section: B Transform Type Selection In Video Codingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DCT and DST Filtering with Sparse Graph Operators

Lu,

Ortega,

Mukherjee

et al. 2021

Preprint

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Polynomial graph filters of multiple shifts and distributed implementation of inverse filtering

Emirov

Cheng

Jiang

et al. 2022

Sampl. Theory Signal Process. Data Anal.

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Polynomial graph filters and their inverses play important roles in graph signal processing. An advantage of polynomial graph filters is that they can be implemented in a distributed manner, which involves data transmission between adjacent vertices only. The challenge arisen in the inverse filtering is that a direct implementation may suffer from high computational burden, as the inverse graph filter usually has full bandwidth even if the original filter has small bandwidth. In this paper, we consider distributed implementation of the inverse filtering procedure for a polynomial graph filter of multiple shifts, and we propose two iterative approximation algorithms that can be implemented in a distributed network, where each vertex is equipped with systems for limited data storage, computation power and data exchanging facility to its adjacent vertices. We also demonstrate the effectiveness of the proposed iterative approximation algorithms to implement the inverse filtering procedure and their satisfactory performance to denoise time-varying graph signals and a data set of US hourly temperature at 218 locations.

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