6533b85efe1ef96bd12c090c
RESEARCH PRODUCT
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring
Martin HankeMarco Donatellisubject
Well-posed problemDeblurringMathematical optimizationIterative methodApplied MathematicsRegularization (mathematics)Computer Science ApplicationsTheoretical Computer ScienceTikhonov regularizationConjugate gradient methodSignal ProcessingApplied mathematicsDeconvolutionMathematical PhysicsLinear least squaresMathematicsdescription
We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems, such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state-of-the-art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional preconditioning.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-08-15 |