Symmetry analysis for a fourth-order noise-reduction partial differential equation

被引：2

作者：

Leach, P. G. L. ^{[1
,2
]}

Paliathanasis, Andronikos ^{[1
,3
]}

机构：

[1] Durban Univ Technol, Inst Syst Sci, POB 1334, ZA-4000 Durban, South Africa

[2] Univ KwaZulu Natal, Sch Math Sci, Durban, South Africa

[3] Univ Austral Chile, Inst Ciencias Fis & Matemat, Valdivia 5090000, Chile

来源：

QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 11期

基金：

新加坡国家研究基金会;

关键词：

Lie symmetries; noise reduction; image processing; NONLOCAL SYMMETRIES; CONSERVATION-LAWS; LIE; CLASSIFICATION; SL(3; R); SYSTEMS; WAVE;

D O I：

10.2989/16073606.2020.1812009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the theory of Lie symmetries in order to study a fourth-order 1+2 evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial differential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe that the reduced fourth-order ordinary differential equations are reduced to second-order ordinary differential equations which are maximally symmetric. Finally, nonstatic closed-form solutions are also determined.

引用

页码：1541 / 1552

页数：12

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