Two directional Laplacian pyramids with application to data imputation

Rabin, Neta; Fishelov, Dalia

doi:10.1007/s10444-019-09697-7

“…In this section, we focus on signal modeling and recovery in the multi-way setting through the lens of optimization, where the graph Laplacian serves the role of imposing signal smoothness. Including graph structures along the modes of multi-way matrices and higher-order tensors has led to more robust and efficient approaches for denoising, matrix completion and inpainting, collaborative filtering, recommendation systems, biclustering, factorization, and dictionary learning [4,16,18,11,10,21]. We begin with dual-graph modeling in the matrix setting and then extend to the higher-order tensor setting.…”

Section: Signal Processing On Multi-way Graphsmentioning

confidence: 99%

“…Further, we review novel multi-way regularizations that are not immediately obvious by viewing the data purely as a tensor. Thus, we synthesize into a coherent family a spectrum of recent and novel MWGSP methods across varied applications in inpainting, denoising, data completion, factor analysis, dictionary learning, and graph learning [10,11,4,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Multiway Graph Signal Processing on Tensors: Integrative Analysis of Irregular Geometries

Stanley

¹

,

Chabrière

²

,

Mishne

³

2020

IEEE Signal Process. Mag.

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Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.

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“…In this section, we focus on signal modeling and recovery in the multi-way setting through the lens of optimization, where the graph Laplacian serves the role of imposing signal smoothness. Including graph structures along the modes of multi-way matrices and higher-order tensors has led to more robust and efficient approaches for denoising, matrix completion and inpainting, collaborative filtering, recommendation systems, biclustering, factorization, and dictionary learning [4,16,18,11,10,21]. We begin with dual-graph modeling in the matrix setting and then extend to the higher-order tensor setting.…”

Section: Signal Processing On Multi-way Graphsmentioning

confidence: 99%

“…Further, we review novel multi-way regularizations that are not immediately obvious by viewing the data purely as a tensor. Thus, we synthesize into a coherent family a spectrum of recent and novel MWGSP methods across varied applications in inpainting, denoising, data completion, factor analysis, dictionary learning, and graph learning [10,11,4,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries

Stanley,

Chi,

Mishne

2020

Preprint

0

View full text Add to dashboard Cite

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures.As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.

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“…This method was introduced in the context of machine learning by Rabin and Coifman in [20], and is modeled after the classical Laplacian pyramids algorithm of Burt and Adelson [10], which is a standard technique in image processing. The LP extension algorithm has been considered in a variety of applications [14,11,24,1,18,12,2], and several variants have been proposed [15,21,22].…”

Section: Introductionmentioning

confidence: 99%