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Электронный каталог: Anikin, I. V. - Inverse Radon Transforms: Analytical and Tikhonov-Like Regularizations of Inversion
Anikin, I. V. - Inverse Radon Transforms: Analytical and Tikhonov-Like Regularizations of Inversion
Статья
Автор: Anikin, I. V.
Modern Physics Letters A [Electronic resource]: Inverse Radon Transforms: Analytical and Tikhonov-Like Regularizations of Inversion
б.г.
ISBN отсутствует
Автор: Anikin, I. V.
Modern Physics Letters A [Electronic resource]: Inverse Radon Transforms: Analytical and Tikhonov-Like Regularizations of Inversion
б.г.
ISBN отсутствует
На полку
Статья
Anikin, I.V.
Inverse Radon Transforms: Analytical and Tikhonov-Like Regularizations of Inversion / I.V.Anikin, X.Chen // Modern Physics Letters A [Electronic resource]. – 2024. – Vol. 39, No. 38. – P. 2450181. – URL: https://doi.org/10.1142/S0217732324501815. – Bibliogr.: 11.
In this paper, we study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore–Penrose’s inversion. By introducing a new analytical term to the Tikhonov regularization of Moore–Penrose’s inversion procedure, we derive new optimization conditions that extend the Tikhonov regularization framework and influence the fitting parameter. This enhancement yields a more robust and accurate reconstruction of physical quantities, demonstrating its potential impact on various studies. We illustrate the significance of new term through schematic examples of physical applications, highlighting its relevance to diverse fields. Our findings provide a valuable tool for improving inversion methods and their applications in physics and beyond.
ОИЯИ = ОИЯИ (JINR)2024
Спец.(статьи,препринты) = С 324.3 - Аксиоматическая теория поля. Аналитические свойства матричных элементов и дисперсионные соотношения. Разложение операторов вблизи светового конуса. Вопросы регуляризации и перенормировки. Размерная регуляризация$
Бюллетени = 10/025
Anikin, I.V.
Inverse Radon Transforms: Analytical and Tikhonov-Like Regularizations of Inversion / I.V.Anikin, X.Chen // Modern Physics Letters A [Electronic resource]. – 2024. – Vol. 39, No. 38. – P. 2450181. – URL: https://doi.org/10.1142/S0217732324501815. – Bibliogr.: 11.
In this paper, we study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore–Penrose’s inversion. By introducing a new analytical term to the Tikhonov regularization of Moore–Penrose’s inversion procedure, we derive new optimization conditions that extend the Tikhonov regularization framework and influence the fitting parameter. This enhancement yields a more robust and accurate reconstruction of physical quantities, demonstrating its potential impact on various studies. We illustrate the significance of new term through schematic examples of physical applications, highlighting its relevance to diverse fields. Our findings provide a valuable tool for improving inversion methods and their applications in physics and beyond.
ОИЯИ = ОИЯИ (JINR)2024
Спец.(статьи,препринты) = С 324.3 - Аксиоматическая теория поля. Аналитические свойства матричных элементов и дисперсионные соотношения. Разложение операторов вблизи светового конуса. Вопросы регуляризации и перенормировки. Размерная регуляризация$
Бюллетени = 10/025
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