Geodesic
Variational image denoising while constraining the distribution of the residual
Electronic transactions on numerical analysis, Tome 42 (2014), pp. 64-84
We present a denoising method aimed at restoring images corrupted by additive noise based on the assumption that the distribution of the noise process is known. The proposed variational model uses Total Variation (TV) regularization (chosen simply for its popularity; any other regularizer could be substituted as well) but constrains the distribution of the residual to fit a given target noise distribution. The residual distribution constraint constitutes the key novelty behind our approach. The restored image is efficiently computed by the constrained minimization of an energy functional using an Alternating Directions Methods of Multipliers (ADMM) procedure. Numerical examples show that the novel residual constraint indeed improves the quality of the image restorations.
Classification : 68U10, 65K10, 65F22, 62E17
Keywords: image denoising, variational models, image residual, probability distribution function 
@article{ETNA_2014__42__a6,
     author = {Lanza,  Alessandro and Morigi,  Serena and Sgallari,  Fiorella and Yezzi,  Anthony J.},
     title = {Variational image denoising while constraining the distribution of the residual},
     journal = {Electronic transactions on numerical analysis},
     pages = {64--84},
     year = {2014},
     volume = {42},
     zbl = {1297.68251},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__42__a6/}
}
TY  - JOUR
AU  - Lanza,  Alessandro
AU  - Morigi,  Serena
AU  - Sgallari,  Fiorella
AU  - Yezzi,  Anthony J.
TI  - Variational image denoising while constraining the distribution of the residual
JO  - Electronic transactions on numerical analysis
PY  - 2014
SP  - 64
EP  - 84
VL  - 42
UR  - http://geodesic.mathdoc.fr/item/ETNA_2014__42__a6/
LA  - en
ID  - ETNA_2014__42__a6
ER  - 
%0 Journal Article
%A Lanza,  Alessandro
%A Morigi,  Serena
%A Sgallari,  Fiorella
%A Yezzi,  Anthony J.
%T Variational image denoising while constraining the distribution of the residual
%J Electronic transactions on numerical analysis
%D 2014
%P 64-84
%V 42
%U http://geodesic.mathdoc.fr/item/ETNA_2014__42__a6/
%G en
%F ETNA_2014__42__a6
Lanza,  Alessandro; Morigi,  Serena; Sgallari,  Fiorella; Yezzi,  Anthony J. Variational image denoising while constraining the distribution of the residual. Electronic transactions on numerical analysis, Tome 42 (2014), pp. 64-84. http://geodesic.mathdoc.fr/item/ETNA_2014__42__a6/