<p style='text-indent:20px;'>In this paper, we propose a new image denosing model to remove the multiplicative noise by a maximum a posteriori estimation and an inhomogeneous fractional <inline-formula><tex-math id="M2">\begin{document}$ 1 $\end{document}</tex-math></inline-formula>-Laplace evolution equation. The main difficulty of the problem is the equation will become very singular when <inline-formula><tex-math id="M3">\begin{document}$ u(x) = u(y) $\end{document}</tex-math></inline-formula>. The existence and uniqueness of the weak positive solution are proved. Numerical examples demonstrate the better capability of our model on some heavy multiplicative noised images.</p>
In this paper, we construct fixed-point algorithms for the second-order total variation models through discretization models and the subdifferential and proximity operators. Particularly, we focus on the convergence conditions of our algorithms by analyzing the eigenvalues of the difference matrix. The algorithms are tested on various images to verify our proposed convergence conditions. The experiments compared with the split Bregman algorithms demonstrate that fixed-point algorithms could solve the second-order functional minimization problem stably and effectively. Keywords Fixed-point algorithm • Convergence • High-order total variation • Image denoising Mathematics Subject Classification 68U10 • 65K10 Supported by NSF of China (11431015), NSF of Guangdong (2016A030313048), ministry of education in Guangdong for excellent young teachers.
The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach. The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated. Result on the uniqueness of the inverse problem is proved. §1 IntroductionThe phenomenon of optical activity in special materials has been known since the beginning of the last century. In recent years chiral materials have been studied intensively in electromagnetic theory literature. Chiral media are examples of media responding with both electric and magnetic polarization to either electric or magnetic excitation. They can be characterized by a set of constitutive relations in which the electric and magnetic fields are coupled. In this paper we use the Drude-Born-Fedorov constitutive equations.Scattering by an obstacle in a chiral medium-although somewhat exotic at a first glanceconstitutes an attractive problem. Some illustrative examples are the turbid chiral media [1] , the Bruggeman homogenization of chiral composites [2] , the method of moments for scattering by a chiral obstacle in a chiral environment [1] ; and the solvability of the latter scattering problem is studied in [3].In this paper, a direct and an inverse scattering problems by a perfectly conducting obstacle in a homogeneous chiral environment are discussed. We confine ourselves to the two-dimensional case.We start our consideration with time-harmonic Maxwell's equationsReceived: 2005-12-16. MR Subject Classification: 65N06.
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