Convergence rates for total variation regularization of coefficient identification problems in elliptic equations II
نویسندگان
چکیده
منابع مشابه
Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization
We propose several formulations for recovering discontinuous coefficients in elliptic problems by using total variation (TV) regularization. The motivation for using TV is its wellestablished ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic outputleast-squares formul...
متن کاملIdentification of Discontinuous Coefficients from Elliptic Problems Using Total Variation Regularization
We propose several formulations for recovering discontinous coeecient of elliptic problems by using total variation (TV) regularization. The motivation for using TV is its well-established ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic output-least-squares formulat...
متن کاملControlled Total Variation regularization for inverse problems
This paper provides a new algorithm for solving inverse problems, based on the minimization of the L2 norm and on the control of the Total Variation. It consists in relaxing the role of the Total Variation in the classical Total Variation minimization approach, which permits us to get better approximation to the inverse problems. The numerical results on the deconvolution problem show that our ...
متن کاملLevel set and total variation regularization for elliptic inverse problems with discontinuous coefficients
We propose a level set approach for elliptic inverse problems with piecewise constant coefficients. The geometry of the discontinuity of the coefficient is represented implicitly by level set functions. The inverse problem is solved using a variational augmented Lagrangian formulation with total variation regularization of the coefficient. The corresponding Euler Lagrange equation gives the evo...
متن کاملAdaptive wavelet methods for elliptic operator equations: Convergence rates
This paper is concerned with the construction and analysis of wavelet-based adaptive algorithms for the numerical solution of elliptic equations. These algorithms approximate the solution u of the equation by a linear combination of N wavelets. Therefore, a benchmark for their performance is provided by the rate of best approximation to u by an arbitrary linear combination of N wavelets (so cal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.11.008