Jiebao Sun

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Fractional-order cross-diffusion system for multiplicative noise removal
- Juanjuan Gao
  School of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
  ,
- Jiebao Sun
  School of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
  ,
- Shengzhu Shi
  School of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
Computers & Mathematics with Applications, Volume 164, Issue C•Jun 2024, pp 1-11 • https://doi.org/10.1016/j.camwa.2024.03.031
Abstract
Multiplicative noise removal is a challenging image processing problem. In this paper, we study a fractional-order nonlinear cross-diffusion system to denoise images corrupted by multiplicative Gamma noise. The system is coupled by two nonlinear, ...
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A Ginzburg-Landau- $H^{- 1}$ Model and Its SAV Algorithm for Image Inpainting
- Xiangyu Bai
  School of Mathematics, Harbin Institute of Technology, Harbin, China
  ,
- Jiebao Sun
  School of Mathematics, Harbin Institute of Technology, Harbin, China
  ,
- Jie Shen
  Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA
  ,
- Wenjuan Yao
  School of Mathematics, Harbin Institute of Technology, Harbin, China
  ,
- Zhichang Guo
  School of Mathematics, Harbin Institute of Technology, Harbin, China
Journal of Scientific Computing, Volume 96, Issue 2•Aug 2023 • https://doi.org/10.1007/s10915-023-02252-z
Abstract
Image inpainting models and the corresponding numerical algorithms play key roles in image processing. At present, the visual output of the oscillatory inpainting area is usually not natural. In this paper, we propose an image inpainting model ... $^{}$ $^{}$
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Fractional-order diffusion model for multiplicative noise removal in texture-rich images and its fast explicit diffusion solving
- Xiujie Shan
  School of Mathematics, Harbin Institute of Technology, 150001, Harbin, China
  ,
- Jiebao Sun
  School of Mathematics, Harbin Institute of Technology, 150001, Harbin, China
  ,
- Zhichang Guo
  School of Mathematics, Harbin Institute of Technology, 150001, Harbin, China
  ,
- Wenjuan Yao
  School of Mathematics, Harbin Institute of Technology, 150001, Harbin, China
  ,
- Zhenyu Zhou
  School of Mathematics, Harbin Institute of Technology, 150001, Harbin, China
BIT, Volume 62, Issue 4•Dec 2022, pp 1319-1354 • https://doi.org/10.1007/s10543-022-00913-3
Abstract
In this paper, we propose a fractional-order anisotropic diffusion model based on fractional Fick’s law for multiplicative noise removal in texture-rich images. A fast explicit diffusion solving algorithm is considered. The new model is different ...
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Nonlocal Adaptive Biharmonic Regularizer for Image Restoration
- Ying Wen
  Harbin Institute of Technology, 150001, Harbin, China
  ,
- Luminita A. Vese
  University of California, 90024, Los Angeles, CA, USA
  ,
- Kehan Shi
  Department of Mathematics, China Jiliang University, 310018, Hangzhou, China
  ,
- Zhichang Guo
  Harbin Institute of Technology, 150001, Harbin, China
  ,
- Jiebao Sun
  Harbin Institute of Technology, 150001, Harbin, China
Journal of Mathematical Imaging and Vision, Volume 65, Issue 3•Jun 2023, pp 453-471 • https://doi.org/10.1007/s10851-022-01129-4
Abstract
In this paper, we propose a nonlocal adaptive biharmonic regularization term for image restoration, combining the advantages of fourth-order models (preserving slopes) and nonlocal methods (preserving textures). Besides the image deblurring and ... $^{}$
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A generalized-Jacobi-function spectral method for space-time fractional reaction-diffusion equations with viscosity terms
- Zhe Yu
  School of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
  ,
- Boying Wu
  School of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
  ,
- Jiebao Sun
  School of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
  ,
- Wenjie Liu
  School of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
Applied Numerical Mathematics, Volume 152, Issue C•Jun 2020, pp 355-378 • https://doi.org/10.1016/j.apnum.2019.11.015
Abstract
In this work, we study a new spectral Petrov-Galerkin approximation of space-time fractional reaction-diffusion equations with viscosity terms built by Riemann-Liouville fractional-order derivatives. The proposed method is reliant on generalized ...
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article
Multiplicative Noise Removal Based on the Smooth Diffusion Equation
- Xiujie Shan
  Department of Mathematics, Harbin Institute of Technology, Harbin, China 150001
  ,
- Jiebao Sun
  Department of Mathematics, Harbin Institute of Technology, Harbin, China 150001
  ,
- Zhichang Guo
  Department of Mathematics, Harbin Institute of Technology, Harbin, China 150001
Journal of Mathematical Imaging and Vision, Volume 61, Issue 6•July 2019, pp 763-779 • https://doi.org/10.1007/s10851-018-00870-z

The multiplicative noise removal problem is of momentous significance in various image processing applications. In this paper, a nonlinear diffusion equation with smooth solution is proposed to remove multiplicative Gamma noise. The diffusion ...
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Multiplicative Noise Removal for Texture Images Based on Adaptive Anisotropic Fractional Diffusion Equations
SIAM Journal on Imaging Sciences, Volume 12, Issue 2, pp 839-873 • https://doi.org/10.1137/18M1187192

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, multiplicative noise destroys almost all information of the original image, especially for texture images. In this paper, a ...
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Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations
- Wenjie Liu
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Jiebao Sun
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Boying Wu
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
Numerical Algorithms, Volume 71, Issue 2•February 2016, pp 437-455 • https://doi.org/10.1007/s11075-015-0002-x

In this paper, we present a high-order accurate method for two-dimensional semilinear parabolic equations. The method is based on a Galerkin-Chebyshev spectral method for discretizing spatial derivatives and a block boundary value methods of fourth-order ...
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A non-divergence diffusion equation for removing impulse noise and mixed Gaussian impulse noise
- Kehan Shi
  Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, PR China
  ,
- Dazhi Zhang
  Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, PR China
  ,
- Zhichang Guo
  Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, PR China
  ,
- Jiebao Sun
  Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, PR China
  ,
- Boying Wu
  Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, PR China
Neurocomputing, Volume 173, Issue P3•January 2016, pp 659-670 • https://doi.org/10.1016/j.neucom.2015.08.012

In this paper, a non-divergence diffusion equation consisting of an impulse noise indicator λ and a regularized Perona-Malik (RPM) diffusion operator is proposed for the removal of impulse noise. The impulse noise indicator λ is designed to keep values ...
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Salt-and-Pepper Noise Removal via Local Hölder Seminorm and Nonlocal Operator for Natural and Texture Image
- Kehan Shi
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Zhichang Guo
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Gang Dong
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Jiebao Sun
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Dazhi Zhang
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
  ,
- Boying Wu
  Department of Mathematics, Harbin Institute of Technology, Harbin, People's Republic of China 150001
Journal of Mathematical Imaging and Vision, Volume 51, Issue 3•March 2015, pp 400-412 • https://doi.org/10.1007/s10851-014-0531-2

Utilizing local Hölder seminorm and nonlocal operator, we propose two efficient salt-and-pepper noise removal algorithms in this paper. We first minimize a local Hölder seminorm based functional which has a great capacity to restore natural images. Then ...
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Adaptive Perona–Malik Model Based on the Variable Exponent for Image Denoising
- Zhichang Guo
  Department of Mathematics, Harbin Institute of Technology, Harbin, China
  ,
- Jiebao Sun
  Department of Mathematics, Harbin Institute of Technology, Harbin, China
  ,
- Dazhi Zhang
  Department of Mathematics, Harbin Institute of Technology, Harbin, China
  ,
- Boying Wu
  Department of Mathematics, Harbin Institute of Technology, Harbin, China
IEEE Transactions on Image Processing, Volume 21, Issue 3•March 2012, pp 958-967 • https://doi.org/10.1109/TIP.2011.2169272

This paper introduces a class of adaptive Perona–Malik (PM) diffusion, which combines the PM equation with the heat equation. The PM equation provides a potential algorithm for image segmentation, noise removal, edge detection, and image enhancement. ...
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A novel variational model for image segmentation
Journal of Computational and Applied Mathematics, Volume 235, Issue 8•February, 2011, pp 2234-2241 • https://doi.org/10.1016/j.cam.2010.10.020

In this paper, we propose a new variational model for image segmentation. Our model is inspired by the complex Ginzburg-Landau model and the semi-norm defined by us. This new model can detect both the convex and concave parts of images. Moreover, it can ...
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An Image Level Set Method for Denoising
IIH-MSP '10: Proceedings of the 2010 Sixth International Conference on Intelligent Information Hiding and Multimedia Signal Processing•October 2010, pp 559-562• https://doi.org/10.1109/IIHMSP.2010.142

In this paper, we propose a new algorithm for image denoising. Our method based on image level set and partial differential equations (PDE) operator. The new method is feasible and easy to implement. Moreover, our method can also retain the key ...
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Periodic doubly degenerate parabolic equation with nonlocal terms
- Jing Li
  Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
  ,
- Jiebao Sun
  Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
  ,
- Boying Wu
  Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
Computers & Mathematics with Applications, Volume 60, Issue 3•August, 2010, pp 490-500 • https://doi.org/10.1016/j.camwa.2010.04.046

This paper is a remark on Gao and Wang (2007) [4]. Under some weaker conditions than [4], we establish the existence of nontrivial nonnegative periodic solutions for a doubly degenerate parabolic equation with nonlocal terms. The key is the use of De ...
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Fractional-order cross-diffusion system for multiplicative noise removal

A Ginzburg-Landau- $H^{- 1}$ Model and Its SAV Algorithm for Image Inpainting

Fractional-order diffusion model for multiplicative noise removal in texture-rich images and its fast explicit diffusion solving

Nonlocal Adaptive Biharmonic Regularizer for Image Restoration

A generalized-Jacobi-function spectral method for space-time fractional reaction-diffusion equations with viscosity terms

Multiplicative Noise Removal Based on the Smooth Diffusion Equation

Multiplicative Noise Removal for Texture Images Based on Adaptive Anisotropic Fractional Diffusion Equations

Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations

A non-divergence diffusion equation for removing impulse noise and mixed Gaussian impulse noise

Salt-and-Pepper Noise Removal via Local Hölder Seminorm and Nonlocal Operator for Natural and Texture Image

Adaptive Perona–Malik Model Based on the Variable Exponent for Image Denoising

A novel variational model for image segmentation

An Image Level Set Method for Denoising

Periodic doubly degenerate parabolic equation with nonlocal terms