Sparsity regularization for electrical impedance tomography: well-posedness and convergence rates
نویسندگان
چکیده
In this paper, we investigate sparsity regularization for electrical impedance tomography (EIT). Here, we combine sparsity regularization with the energy functional approach. The main results of our paper is the well-posedness and convergence rates of the sparsity regularization method.
منابع مشابه
Sparsity regularization of the diffusion coefficient problem: well-posedness and convergence rates
In this paper, we investigate sparsity regularization for the diffusion coefficient identification problem. Here, the regularization method is incorporated with the energy functional approach. The advantages of our approach are to deal with convex minimization problems. Therefore, the well-posedness of the problem is obtained without requiring regularity property of the parameter. The convexity...
متن کاملRegularization by dynamic programming
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization properties and also obtain rates of convergence for our methods. A numerical example concerning a dynamical electrical impedance tomography (EIT) problem is used t...
متن کاملElectrical Impedance Tomography Image Reconstruction Using Iterative Lavrentiev and L-Curve-Based Regularization Algorithm
Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse pro...
متن کاملA Convergence Analysis of the Newton-type Regularization Cg-reginn with Application to Impedance Tomography
The Newton-type regularization CG-REGINN is an efficient tool for stably solving nonlinear ill-posed problems. In this paper a new convergence analysis for a slightly modified version of CG-REGINN is given, extending previous results by Hanke [Numer. Funct. Anal. Optimiz. 18, 971-993, 1997] and the second author [SIAM Numer. Anal. 43, 604-622, 2005]. Some numerical experiments from electrical i...
متن کاملJoint L and Total Variation Regularization for Magnetic Detection Electrical Impedance Tomography
─ Magnetic detection electrical impedance tomography (MDEIT) is an imaging modality that aims to compute the cross-sectional distribution of the conductivity of a volume from the magnetic flux density surrounding the object. Owing to the Biot-Savart law, the MDEIT inverse problem is inherently ill-conditioned making image reconstruction highly susceptible to the effects of noise and numerical e...
متن کامل