Variable Exponent, Linear Growth Functionals in Image Restoration

By Yunmei Chen, Stacey Levine, Murali Rao. SIAM Journal on Applied Mathematics, 2006

1,772 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f07ccd755ce507f2fcfe228c9cee19f1b3a02a49

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Citations in the corpus

Anisotropic nonlinear Neumann problems (2011, methodology): “We mention the works of Acerbi– Mingione [1,2], Cheng–Levine–Rao [ 10 ], Marcellini [31], Ruziycka [36], Zhikov [39].”
Generalized Orlicz spaces and related PDE (2016, background): “In addition to being a natural generalization which covers r sults from both variable exponent and Orlicz spaces, the study of generalized Orlicz spaces can be motivated by applications to image processing [2, 6, 16], fluid dynamic s [33, 34] and differential equations.”
Extrapolation and interpolation in generalized Orlicz spaces (2018, background): “They have appeared in many problems in PDEs and the calculus of variations [4, 5, 6, 13, 27] and have applications to image processing [10, 32, 37] and fluid dynamics [53].”
Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, background): “We refer the reader to [18] and the references therein.”
Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, background): “In addition, it provides a theoretical background on the studies of electrorheological fluid dynamics [1, 2, 61, 63, 64] and imaging processing [11].”
Hölder estimates for parabolic p(x, t)-Laplacian systems (2012, background): “Finally, related applications in the stationary case arise in non-linear elasticity [32] and image processing [11].”
Nonlinear elliptic equations with variable exponent: Old and new (2015, methodology): “For more information on properties, modeling and the application of variable exponent spaces to these fluids we refer to Acerbi and Mingione [1], Ruzicka [42], Chen, Levine, and Rao [9], Harjulehto, Hästö, Latvala, and Toivanen [20], Molica Bisci and Repovš [34], et al. We also point out the pioneer”
Calderón–Zygmund type estimates for a class of obstacle problems with p(x) growth (2010, background): “…of an increasing number of mathematicians in the past 15 years for a variety of reasons: on one hand they represent a borderline case between standard p growth conditions (with constant exponent) and so–called p − q growth condition introduced by Marcellini [33], on the other hand they appear…”
On the removability of isolated singular points for elliptic equations involving variable exponent (2015, background): “In the studies of electrorheological fluid, nonlinear elasticity and image restoration in practical applications, the classical Lebesgue and Sobolev spaces are not applicable, see [1, 5, 18].”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Typical examples of equations involving the variable exponent setting include models of electrorheological fluids [3, 175, 177], image restoration processing [43], elasticity equations [201], and thermistor model [202].”