Geodesic
Noise propagation in regularizing iterations for image deblurring
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 204-220
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.
Classification : 65F22, 65F10
Keywords: image deblurring, regularizing iterations, Krylov subspaces, CGLS, LSQR, GMRES, MINRES, RRGMRES, MR-II 
@article{ETNA_2008__31__a10,
     author = {Hansen,  Per Christian and Jensen,  Toke Koldborg},
     title = {Noise propagation in regularizing iterations for image deblurring},
     journal = {Electronic transactions on numerical analysis},
     pages = {204--220},
     year = {2008},
     volume = {31},
     zbl = {1171.65032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a10/}
}
TY  - JOUR
AU  - Hansen,  Per Christian
AU  - Jensen,  Toke Koldborg
TI  - Noise propagation in regularizing iterations for image deblurring
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 204
EP  - 220
VL  - 31
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__31__a10/
LA  - en
ID  - ETNA_2008__31__a10
ER  - 
%0 Journal Article
%A Hansen,  Per Christian
%A Jensen,  Toke Koldborg
%T Noise propagation in regularizing iterations for image deblurring
%J Electronic transactions on numerical analysis
%D 2008
%P 204-220
%V 31
%U http://geodesic.mathdoc.fr/item/ETNA_2008__31__a10/
%G en
%F ETNA_2008__31__a10
Hansen,  Per Christian; Jensen,  Toke Koldborg. Noise propagation in regularizing iterations for image deblurring. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 204-220. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a10/