Fractional partial differential equation: fractional total variation and fractional steepest descent approach-based multiscale denoising model for texture image
type: Item
instance of: scholarly article
title: Fractional partial differential equation: fractional total variation and fractional steepest descent approach-based multiscale denoising model for texture image
zbMATH Open document ID: 1381.35231
DOI: 10.1155/2013/483791
author: Yi-Fei Pu
author: Ji-Liu Zhou
author: Patrick Siarry
author: Ni Zhang
author: Yiguang Liu
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method-fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green's formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35Q94
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 6306870
Wikidata QID: Q58916400
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/483791
OpenAlex ID: W2037580505
cites work: Fractional Derivatives of Imaginary Order
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Q3141895
cites work: Derivatives of Noninteger Order
cites work: Q4726489
cites work: On fractional calculus and fractional multipoles in electromagnetism
cites work: Fractional calculus operators and their applications involving power functions and summation of series
cites work: An introduction to fractional calculus
cites work: Fractional calculus via functional calculus: Theory and applications
cites work: Q5699297
cites work: Advances in Fractional Calculus
cites work: Applications of Fractional Calculus to the Theory of Viscoelasticity
cites work: A suggestion of fractional-order controller for flexible spacecraft attitude control
cites work: A new IIR-type digital fractional order differentiator
cites work: Q4813356
cites work: Scale Space and PDE Methods in Computer Vision
cites work: Fractional Splines and Wavelets
cites work: Estimation of 1/f noise
cites work: Fractional differentiation for edge detection
cites work: A novel approach for multi-scale texture segmentation based on fractional differential
cites work: Fractional Differential Mask: A Fractional Differential-Based Approach for Multiscale Texture Enhancement
cites work: A Review of Image Denoising Algorithms, with a New One
cites work: Q4375274
cites work: Nonlinear total variation based noise removal algorithms
cites work: Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement
cites work: Scale Recognition, Regularization Parameter Selection, and Meyer's G Norm in Total Variation Regularization
cites work: Selection of optimal stopping time for nonlinear diffusion filtering
cites work: Iterative Methods for Total Variation Denoising
cites work: Combinatorial Image Analysis
cites work: Image restoration with discrete constrained total variation. I: Fast and exact optimization
cites work: Image restoration with discrete constrained total variation. II: Levelable functions, convex priors and non-convex cases
cites work: Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
cites work: Oscillating patterns in image processing and nonlinear evolution equations. The fifteenth Dean Jacqueline B. Lewis memorial lectures
cites work: Edge-preserving and scale-dependent properties of total variation regularization
cites work: A variational approach to remove outliers and impulse noise
cites work: Aspects of Total Variation RegularizedL1Function Approximation
cites work: Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers
cites work: An Iterative Regularization Method for Total Variation-Based Image Restoration
cites work: Decomposition of images by the anisotropic Rudin-Osher-Fatemi model
cites work: Pseudospectra of semiclassical (pseudo-) differential operators
cites work: High-Order Total Variation-Based Image Restoration
cites work: Fourth-order partial differential equations for noise removal
cites work: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time
cites work: Image recovery via total variation minimization and related problems
cites work: Image Decomposition and Restoration Using Total Variation Minimization and theH1
cites work: Iterative image restoration combining total variation minimization and a second-order functional
cites work: Noise Removal Using Smoothed Normals and Surface Fitting
cites work: A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section
cites work: The calculus of variations and optimal control. An introduction
cites work: Fractional vector calculus and fractional Maxwell's equations
cites work: Q4340096
cites work: Multiresolution Bilateral Filtering for Image Denoising
cites work: Image Denoising Using Trivariate Shrinkage Filter in the Wavelet Domain and Joint Bilateral Filter in the Spatial Domain
cites work: Q5558293
cites work: Q5799972
cites work: Q5817554
description: scientific article; zbMATH DE number 6306870