Existence of infinitely many solutions for the one-dimensional Perona-Malik model

被引：46
|
作者：
Zhang, KW [1 ]
机构：
[1] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 26卷 / 02期
关键词：
Perona-Malik model; one-dimensional; infinitely many solutions; differential inclusion; relaxation property;
D O I：
10.1007/s00526-005-0363-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem.
引用
收藏
页码：171 / 199
页数：29
相关论文
共 50 条
  • [21] The existence of countably many positive solutions for one-dimensional p-Laplacian with infinitely many singularities on the half-line
    Liang, Sihua
    Zhang, Jihui
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 201 (1-2) : 210 - 220
  • [22] Perona-Malik model with self-adjusting shape-defining constant
    Maiseli, Baraka
    Msuya, Hubert
    Kessy, Suzan
    Kisangiri, Michael
    INFORMATION PROCESSING LETTERS, 2018, 137 : 26 - 32
  • [23] Image denoising using modified Perona-Malik model based on directional Laplacian
    Wang, Y. Q.
    Guo, Jichang
    Chen, Wufan
    Zhang, Wenxue
    SIGNAL PROCESSING, 2013, 93 (09) : 2548 - 2558
  • [24] Image Denoising using Variations of Perona-Malik Model with different Edge Stopping Functions
    Kamalaveni, V.
    Rajalakshmi, R. Anitha
    Narayanankutty, K. A.
    SECOND INTERNATIONAL SYMPOSIUM ON COMPUTER VISION AND THE INTERNET (VISIONNET'15), 2015, 58 : 673 - 682
  • [25] IMAGE RESTORATION USING A NOVEL MODEL COMBINING THE PERONA-MALIK EQUATION AND THE HEAT EQUATION
    Lecheheb, Samira
    Maouni, Messaoud
    Lakhal, Hakim
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2021, 19 (02): : 228 - 238
  • [26] Non-local means theory based Perona-Malik model for image denosing
    Yang, Min
    Liang, Jingkun
    Zhang, Jianhai
    Gao, Haidong
    Meng, Fanyong
    Li, Xingdong
    Song, Sung-Jin
    NEUROCOMPUTING, 2013, 120 : 262 - 267
  • [27] A Hybrid Model for Image Denoising Combining Modified Isotropic Diffusion Model and Modified Perona-Malik Model
    Wang, Na
    Shang, Yu
    Chen, Yang
    Yang, Min
    Zhang, Quan
    Liu, Yi
    Gui, Zhiguo
    IEEE ACCESS, 2018, 6 : 33568 - 33582
  • [28] Existence of solutions to a model for sparse, one-dimensional fluids
    Hoff, David
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (02) : 1083 - 1113
  • [29] On existence of infinitely many homoclinic solutions
    Wójcik, K
    Zgliczynski, P
    MONATSHEFTE FUR MATHEMATIK, 2000, 130 (02): : 155 - 160
  • [30] On Existence of Infinitely Many Homoclinic Solutions
    Klaudiusz Wójcik
    Piotr Zgliczyński
    Monatshefte für Mathematik, 2000, 130 : 155 - 160
12345