Fetching the paper…
Reading the bibliography…
In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the Riemann-Liouville fractional derivative.
Fractional integrals and derivatives
S. G. Samko, A. A. Kilbas, and O. I. Marichev · 1987
Earlier work this paper cites.
Nonlinear total variation based noise removal algorithms
L. I. Rudin, S. Osher, and E. Fatemi · 1991
Earlier work this paper cites.
An introduction to the fractional calculus and fractional differential equations
K. S. Miller and B. Ross · 1993
Earlier work this paper cites.
Matrix approach to discrete fractional calculus
I. Podlubny · 2000
Earlier work this paper cites.
Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results
G. Jumarie · 2006
Earlier work this paper cites.
Fractional variational calculus in terms of riesz fractional derivatives
O. P. Agrawal · 2007
Earlier work this paper cites.
Utilizing variational optimization to learn markov random fields
M. F. Tappen · 2007
Cited alongside, same era.
Learning gaussian conditional random fields for low-level vision
M. F. Tappen, C. Liu, E. H. Adelson, and W. T. Freeman · 2007
Cited alongside, same era.
Functional analysis, Sobolev spaces and partial differential equations
H. Brezis · 2011
Cited alongside, same era.
Generic methods for optimization-based modeling
J. Domke · 2012
Cited alongside, same era.
Fractional-order T V TV - L 2 L^{2} model for image denoising
D. Chen, S. Sun, C. Zhang, Y. Chen, and D. Xue · 2013
Cited alongside, same era.
Learning graphical model parameters with approximate marginal inference
J. Domke · 2013
Cited alongside, same era.
Fractional Sobolev spaces via Riemann-Liouville derivatives
D. Idczak and S. a. Walczak · 2013
Later among the works it cites.
Measure theory and fine properties of functions
L. C. Evans and R. F. Gariepy · 2015
Later among the works it cites.
A total fractional-order variation model for image restoration with nonhomogeneous boundary conditions and its numerical solution
J. Zhang and K. Chen · 2015
Later among the works it cites.
Fractional Sobolev spaces and functions of bounded variation of one variable
M. Bergounioux, A. Leaci, G. Nardi, and F. Tomarelli · 2017
Later among the works it cites.
One dimensional fractional order T G V TGV : gamma-convergence and bilevel training scheme
E. Davoli and P. Liu · 2018
Closest in time.
A generalized definition of caputo derivatives and its application to fractional odes
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Real order (an)-isotropic total variation in image processing - Part II: Gamma convergence and learning of optimal orders
X. Y. Lu and P. Liu
Cited in the paper.
L. Li and J. Liu · 2018
Closest in time.