Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Electrical Impedance Tomography
SIAM Review
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Neuro-Dynamic Programming
Inexact Newton Regularization Using Conjugate Gradients as Inner Iteration
SIAM Journal on Numerical Analysis
On Effective Methods for Implicit Piecewise Smooth Surface Recovery
SIAM Journal on Scientific Computing
On level set regularization for highly ill-posed distributed parameter estimation problems
Journal of Computational Physics
Robust Stochastic Approximation Approach to Stochastic Programming
SIAM Journal on Optimization
Towards a general convergence theory for inexact Newton regularizations
Numerische Mathematik
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This article develops fast numerical methods for the practical solution of the famous electrical impedance tomography and DC resistivity problems in the presence of discontinuities and potentially many experiments or data. Based on a Gauss-Newton (GN) approach coupled with preconditioned conjugate gradient (PCG) iterations, we propose two algorithms. One determines adaptively the number of inner PCG iterations required to stably and effectively carry out each GN iteration. The other algorithm, useful especially in the presence of many experiments, employs a randomly chosen subset of experiments at each GN iteration that is controlled using a cross validation approach. Numerical examples demonstrate the efficacy of our algorithms.