Volume 31, pp. 204-220, 2008.

Noise propagation in regularizing iterations for image deblurring

Per Christian Hansen and Toke Koldborg Jensen

Abstract

We use the two-dimensional discrete cosine transform to study how the noise from the data enters the reconstructed images computed by regularizing iterations, that is, Krylov subspace methods applied to discrete ill-posed problems. The regularization in these methods is obtained via the projection onto the associated Krylov subspace. We focus on CGLS/LSQR, GMRES, and RRGMRES, as well as MINRES and MR-II in the symmetric case. Our analysis shows that the noise enters primarily in the form of band-pass filtered white noise, which appears as “freckles” in the reconstructions, and these artifacts are present in both the signal and the noise components of the solutions. We also show why GMRES and MINRES are not suited for image deblurring.

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Key words

Image deblurring, regularizing iterations, Krylov subspaces, CGLS, LSQR, GMRES, MINRES, RRGMRES, MR-II.

AMS subject classifications

65F22, 65F10.

ETNA articles which cite this article

Vol. 41 (2014), pp. 465-477 Donghui Chen, Misha E. Kilmer, and Per Christian Hansen: “Plug-and-Play” Edge-Preserving Regularization
Vol. 44 (2015), pp. 83-123 Silvia Gazzola, Paolo Novati, and Maria Rosaria Russo: On Krylov projection methods and Tikhonov regularization

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