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

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

6 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Título de la publicación alojada	2022 45th International Conference on Telecommunications and Signal Processing, TSP 2022
Editores	Norbert Herencsar
Editorial	Institute of Electrical and Electronics Engineers Inc.
Páginas	59-65
Número de páginas	7
ISBN (versión digital)	9781665469487
DOI	https://doi.org/10.1109/TSP55681.2022.9851367
Estado	Publicada - 2022
Evento	45th International Conference on Telecommunications and Signal Processing, TSP 2022 - Virtual, Online, República Checa Duración: 13 jul 2022 → 15 jul 2022

Serie de la publicación

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

Conferencia

Conferencia	45th International Conference on Telecommunications and Signal Processing, TSP 2022
País/Territorio	República Checa
Ciudad	Virtual, Online
Período	13/07/22 → 15/07/22

Acceder al documento

10.1109/TSP55681.2022.9851367

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Enlace a la publicación en Scopus

Gen-FW: Una generalización del problema de Fermat-Weber con aplicaciones al procesamiento de datos
Torokhti, A. (Persona académica coordinadora institucional), Soto-Quiros, P. (Persona académica coordinadora institucional), Figueroa Mata, G. (Persona académica coordinadora institucional) & Valverde-Otárola, J. C. (Persona académica coordinadora institucional)
1/01/20 → 31/12/21
Proyecto: Proyectos Investigación Con fondos internos › Investigación básica y aplicada

Citar esto

Soto-Quiros, P. (2022). A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. En 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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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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Soto-Quiros, P 2022, A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. En 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, República Checa, 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).

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

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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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Soto-Quiros P. A Least-Squares Problem of a Linear Tensor Equation of Third-Order for Audio and Color Image Processing. En 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

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Proyectos

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

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