MATHEMATICAL MODEL USED TO IMPROVE IMAGE QUALITY
Keywords:
image, piecewise polynomial methods, cubic Hermite spline, local spline functions.Abstract
The study examined the use of piecewise polynomial methods in digital image processing. A Hermitian spline function of piecewise polynomials is selected as a mathematical model for digital signal processing, and the construction of a third-order Hermitian spline function with two variables is presented. Based on the constructed mathematical model, an image restoration algorithm has been developed.
References
Завьялов Ю.С., Квасов Б.И., Мирошниченко В.Л. Методы сплайн-функций. Москва: Наука, 1980. - 352 с.
Зайниддинов Х.Н. Методы и средства обработки сигналов в кусочно полиномиальных базисах. 2015, Тошкент. - С. 29-40.
Xakimjon, Z., & Bunyod, A. (2019). Biomedical signals interpolation spline models. In International Conference on Information Science and Communications Technologies: Applications, Trends and Opportunities, ICISCT 2019. Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/ICISCT47635.2019.9011926.
Азимов Б.Р. Натурал ва локал кубик сплайнлар орқали сигналларга рақамли ишлов бериш // Бухоро мухандислик технологиялари институти илмий-техника журнали. 2020, Бухоро. –.Б 125-132.
Y. A. Üncü, T. Mercan, G. Sevym, and M. Canpolat, “Interpolation applications in diffuse optical tomography system,” 2018, doi: 10.1109/BIYOMUT.2017.8478855.
J.S. Lim, Two-dimensional signal and image processing, 1990.
V. Graffigna, C. Brunini, M. Gende, M. Hernández-Pajares, R. Galván, F. Oreiro, “Retrieving geophysical signals from GPS in the La Plata River region,” GPS Solutions, 23(3), 2019, doi:10.1007/s10291-019-0875-6.
X. Wang, Z. Luo, B. Zhong, Y. Wu, Z. Huang, H. Zhou, Q. Li, “Separation and recovery of geophysical signals based on the Kalman Filter with GRACE gravity data,” Remote Sensing, 11(4), 2019, doi:10.3390/rs11040393.
A.I. Grebennikov, “Isogeometric approximation of functions of one variable,” USSR Computational Mathematics and Mathematical Physics, 22(6), 1982, doi:10.1016/0041-5553(82)90095-7.
Kroizer, Y.C. Eldar, T. Routtenberg, “Modeling and recovery of graph signals and difference-based signals,” in GlobalSIP 2019 - 7th IEEE Global Conference on Signal and Information Processing, Proceedings, 2019, doi:10.1109/GlobalSIP45357.2019.8969536.
Алберг Дж., Нильсон Э., Уолш Дж. Теория сплайнов и ее приложения. Москва: Мир, 1972. – 316 с.
Стечкин С.Б., Субботин Ю.Н. Сплайны в вычислительной математике. Москва, Наука, 1976. – 248 с.
