A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing

Pablo Soto-Quiros

doi:10.1109/TSP55681.2022.9851367

A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing

Pablo Soto-Quiros

Escuela de Matemática

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

This paper describes a new framework for solving inverse tensor problems for denoising data. This inverse tensor problem can be represented as a least-squares problem of a linear tensor equation of third-order. We use training data to replace knowledge of the noise model by introducing a framework that avoids including a particular noise model. Additionally, we describe a numerical method based on a tensor pseudoinverse to estimate a solution to the least-squares problem. Finally, we present two real-life applications for audio denoising and color image deconvolution. The advantages of the considered technique are discussed and illustrated numerically.

Original language	English
Title of host publication	2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022
Editors	Norbert Herencsar
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	59-65
Number of pages	7
ISBN (Electronic)	9781665469487
DOIs	https://doi.org/10.1109/TSP55681.2022.9851367
State	Published - 2022
Event	45th International Conference on Telecommunications and Signal Processing, TSP 2022 - Virtual, Online, Czech Republic Duration: 13 Jul 2022 → 15 Jul 2022

Publication series

Name	2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022

Conference

Conference	45th International Conference on Telecommunications and Signal Processing, TSP 2022
Country/Territory	Czech Republic
City	Virtual, Online
Period	13/07/22 → 15/07/22

Keywords

De-noising Data
Least-Squares Problem
Third-Order Tensor
Training Data

Access to Document

10.1109/TSP55681.2022.9851367

Cite this

Soto-Quiros, P. (2022). A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. In N. Herencsar (Ed.), 2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022 (pp. 59-65). (2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/TSP55681.2022.9851367

Soto-Quiros, Pablo. / A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. 2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022. editor / Norbert Herencsar. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 59-65 (2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022).

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title = "A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing",

abstract = "This paper describes a new framework for solving inverse tensor problems for denoising data. This inverse tensor problem can be represented as a least-squares problem of a linear tensor equation of third-order. We use training data to replace knowledge of the noise model by introducing a framework that avoids including a particular noise model. Additionally, we describe a numerical method based on a tensor pseudoinverse to estimate a solution to the least-squares problem. Finally, we present two real-life applications for audio denoising and color image deconvolution. The advantages of the considered technique are discussed and illustrated numerically.",

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series = "2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022",

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Soto-Quiros, P 2022, A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. in N Herencsar (ed.), 2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022. 2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022, Institute of Electrical and Electronics Engineers Inc., pp. 59-65, 45th International Conference on Telecommunications and Signal Processing, TSP 2022, Virtual, Online, Czech Republic, 13/07/22. https://doi.org/10.1109/TSP55681.2022.9851367

A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. / Soto-Quiros, Pablo.
2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022. ed. / Norbert Herencsar. Institute of Electrical and Electronics Engineers Inc., 2022. p. 59-65 (2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - This paper describes a new framework for solving inverse tensor problems for denoising data. This inverse tensor problem can be represented as a least-squares problem of a linear tensor equation of third-order. We use training data to replace knowledge of the noise model by introducing a framework that avoids including a particular noise model. Additionally, we describe a numerical method based on a tensor pseudoinverse to estimate a solution to the least-squares problem. Finally, we present two real-life applications for audio denoising and color image deconvolution. The advantages of the considered technique are discussed and illustrated numerically.

AB - This paper describes a new framework for solving inverse tensor problems for denoising data. This inverse tensor problem can be represented as a least-squares problem of a linear tensor equation of third-order. We use training data to replace knowledge of the noise model by introducing a framework that avoids including a particular noise model. Additionally, we describe a numerical method based on a tensor pseudoinverse to estimate a solution to the least-squares problem. Finally, we present two real-life applications for audio denoising and color image deconvolution. The advantages of the considered technique are discussed and illustrated numerically.

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KW - Least-Squares Problem

KW - Third-Order Tensor

KW - Training Data

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M3 - Contribución a la conferencia

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Soto-Quiros P. A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. In Herencsar N, editor, 2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022. Institute of Electrical and Electronics Engineers Inc. 2022. p. 59-65. (2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022). doi: 10.1109/TSP55681.2022.9851367

A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Gen-FW: Una generalización del problema de Fermat-Weber con aplicaciones al procesamiento de datos

Cite this

A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Gen-FW: Una generalización del problema de Fermat-Weber con aplicaciones al procesamiento de datos

Cite this