A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising
Zhang Jun,Wei Zhihui +1 more
TLDR
In this paper, the authors proposed a new space of functions of fractional-order bounded variation called the BV α space by using the Grunwald-Letnikov definition of fractiona-order derivative, which can improve the peak signal to noise ratio of image, preserve textures and eliminate the staircase effect.About:
This article is published in Applied Mathematical Modelling.The article was published on 2011-05-01 and is currently open access. It has received 109 citations till now. The article focuses on the topics: Total variation denoising & Image restoration.read more
Citations
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A new collection of real world applications of fractional calculus in science and engineering
TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.
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Fractional calculus in image processing: a review
TL;DR: In this paper, a review of fractional-order based methods for image processing is presented, which includes image enhancement, image denoising, image edge detection, image segmentation, image registration, image recognition, image fusion, image encryption, image compression and image restoration.
Posted Content
Fractional Calculus In Image Processing: A Review
TL;DR: It is well proved that as a fundamental mathematic tool, fractional-order derivative shows great success in image processing.
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Fractional order total variation regularization for image super-resolution
TL;DR: A fractional order total variation (TV) regularization functional for image super-resolution is presented, the role of which is to better handle the texture details of image to efficiently preserve the discontinuities and image structures.
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An improved fractional-order differentiation model for image denoising
TL;DR: An improved model based on the Grunwald-Letnikov (G-L) fractional differential operator based on G-L fractional order differentiation is proposed for image denoising and successfully used to denoise three-dimensional magnetic resonance images.
References
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Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
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Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time
TL;DR: A new method for image smoothing based on a fourth-order PDE model that demonstrates good noise suppression without destruction of important anatomical or functional detail, even at poor signal-to-noise ratio is introduced.
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Fourth-order partial differential equations for noise removal
Yu-Li You,Mostafa Kaveh +1 more
TL;DR: A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation, and speckles are more visible in images processed by the proposed PDEs, because piecewise planar images are less likely to mask speckling.