F. Drira, Towards Restoring Historic Documents Degraded Over Time, Second International Conference on Document Image Analysis for Libraries (DIAL'06), pp.350-357, 2006.
DOI : 10.1109/DIAL.2006.43

M. Cannon, J. Hochberg, and P. Kelly, Quality assessment and restoration of typewritten document images, International Journal on Document Analysis and Recognition, vol.2, issue.2-3, pp.80-89, 1999.
DOI : 10.1007/s100320050039

V. Aurich and J. , Weule: Non-linear gaussian filters performing edge preserving diffusion, Proceedings of the DAGM Symposium, pp.538-545, 1995.
DOI : 10.1007/978-3-642-79980-8_63

L. Rudin and S. Osher, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

A. Buades, B. Coll, and J. , A Non-Local Algorithm for Image Denoising, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)
DOI : 10.1109/CVPR.2005.38

. Fig, 45 Restoration of a natural image (classical image of Lena) with the proposed filter; respectively from left to right, details before and after restoration

. Fig, 46 From left to right respectively : Original image and its restored version with our proposed diffusion filter, ference on Computer Vision and Pattern Recognition (CVPR), pp.60-65, 2005.

A. Buades, B. Coll, and J. , A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.290-530, 2005.
DOI : 10.1137/040616024

URL : https://hal.archives-ouvertes.fr/hal-00271141

A. Dauwe, B. Goossens, H. Luong, and W. Philips, A fast non-local image denoising algorithm, Image Processing: Algorithms and Systems VI, 2008.
DOI : 10.1117/12.765505

P. Coup, P. Yger, S. Prima, P. Hellier, C. Kervrann et al., An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images, IEEE Transactions on Medical Imaging, vol.27, issue.4, pp.425-441, 2008.
DOI : 10.1109/TMI.2007.906087

P. Chatterjee and P. Milanfar, A generalization of non-local means via kernel regression, Computational Imaging VI, 2008.
DOI : 10.1117/12.778615

S. Zimmer, S. Didas, and J. Weickert, A rotationally invariant block matching strategy improving image denoising with non-local means, Proceedings of International Workshop on Local andNon-Local Approximation in Image Processing, pp.135-142, 2008.

. Fig, 47 From left to right respectively : Original image and its restored version with our proposed diffusion filter

. Fig, 48 From left to right respectively : Original medical image and its restored version with our proposed diffusion filter

M. Aharon, M. Elad, and A. Bruckstein, <tex>$rm K$</tex>-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation, IEEE Transactions on Signal Processing, vol.54, issue.11, pp.4311-4322, 2006.
DOI : 10.1109/TSP.2006.881199

R. Nakagaki and A. Katsaggelos, A VQ-based blind image restoration algorithm, IEEE Transactions on Image Processing, vol.12, issue.9, pp.1044-1053, 2003.
DOI : 10.1109/TIP.2003.816007

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.3067

S. Roth and M. J. , Fields of Experts, International Journal of Computer Vision, vol.27, issue.2, pp.205-229, 2009.
DOI : 10.1007/s11263-008-0197-6

J. Mairal, M. Elad, and G. Sapiro, Sparse Representation for Color Image Restoration, IEEE Transactions on Image Processing, vol.17, issue.1, pp.53-69, 2008.
DOI : 10.1109/TIP.2007.911828

H. Nishida, Restoring high-resolution binary images for text enhancement, IEEE International Conference on Image Processing 2005, pp.506-509, 2005.
DOI : 10.1109/ICIP.2005.1530103

Q. Zheng and T. Kanungo, Morphological degradation models and their use in document image restoration, ICIP'01, pp.193-196, 2001.

J. Liang and R. M. Haralick, Document image restoration using binary morphological filters, SPIE'96, pp.274-285, 1996.
DOI : 10.1117/12.234709

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.1300

F. Sattar and D. Tay, Enhancement of document images using multiresolution and fuzzy logic techniques, IEEE Signal Processing Letters, vol.6, issue.10, pp.249-252, 1999.
DOI : 10.1109/97.789601

Z. Shi and V. Govindaraju, Historical document image enhancement using background light intensity normalization, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., pp.473-476, 2004.
DOI : 10.1109/ICPR.2004.1334167

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.524.7368

P. Sarkar, H. Baird, and X. Zhang, Training on severely degraded text-line images, Proceedings of the International Conference on Document Analysis and Recognition, pp.38-43, 2003.

A. Tonazzini, S. Vezzosi, and L. Bedini, Analysis and recognition of highly degraded printed characters, International Journal on Document Analysis and Recognition, vol.6, issue.4, pp.236-247, 2004.
DOI : 10.1007/s10032-003-0115-y

H. Luong and W. Philips, Non-Local Text Image Reconstruction, Ninth International Conference on Document Analysis and Recognition (ICDAR 2007), pp.546-550, 2007.
DOI : 10.1109/ICDAR.2007.4378769

J. Banerjee, A. M. Namboodiri, and C. V. Jawahar, Contextual restoration of severely degraded document images, 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp.517-524, 2009.
DOI : 10.1109/CVPR.2009.5206601

A. Tonazzini, E. Salerno, and L. Bedini, Fast correction of bleed-through distortion in grayscale documents by a blind source separation technique, International Journal of Document Analysis and Recognition (IJDAR), vol.13, issue.1, pp.17-25, 2007.
DOI : 10.1007/s10032-006-0015-z

C. Wolf, Document Ink Bleed-Through Removal with Two Hidden Markov Random Fields and a Single Observation Field, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.3, pp.431-447, 2010.
DOI : 10.1109/TPAMI.2009.33

URL : https://hal.archives-ouvertes.fr/hal-01381428

R. F. Moghaddam and M. Cheriet, RSLDI: Restoration of single-sided low-quality document images, Pattern Recognition, Special Issue on Handwriting Recognition, pp.3355-3364, 2009.

I. Nwogu, Z. Shi, and V. Govindaraju, PDE-Based Enhancement of Low Quality Documents, Ninth International Conference on Document Analysis and Recognition (ICDAR 2007), pp.541-545, 2007.
DOI : 10.1109/ICDAR.2007.4378768

F. Drira, F. Lebourgeois, and H. Emptoz, Restoring Ink Bleed-Through Degraded Document Images Using a Recursive Unsupervised Classification Technique, DAS'2006, pp.38-49, 2006.

F. Drira and H. Lebourgeois, Emptoz : A Modified Mean Shift Algorithm For Efficient Document Image Restoration, In Signal processing for image enhancement and multimedia processing Ed, pp.978-978, 2008.

A. Ledda, A. Ledda, H. Q. Luong, W. Philips, V. De-witte et al., Greyscale Image Interpolation Using Mathematical Morphology, Proceedings of ACIVS (LNCS 4179), pp.78-90, 2006.
DOI : 10.1007/11864349_8

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.4900

J. D. Hobby, H. S. Baird, Q. Zheng, and T. Kanungo, Morphological degradation models and their use in document image restoration, pp.193-196, 2001.

J. D. Hobby and H. S. Baird, Degraded Character Image Restoration, Proc. of Document Analysis and Information Retrieval, 1996.

H. S. Baird, State of the Art of Document Image Degradation Modeling, Proceedings of 4th IAPR International Workshop on Document Analysis Systems, 2000.

J. D. Hobby and T. K. Ho, Enhancing degraded document images via bitmap clustering and averaging, Proceedings of the Fourth International Conference on Document Analysis and Recognition, pp.394-400, 1997.
DOI : 10.1109/ICDAR.1997.619877

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.2730

A. Whichello and H. Yan, Linking broken character borders with variable sized masks to improve recognition, Pattern Recognition, vol.29, issue.8, pp.1429-1435, 1996.
DOI : 10.1016/0031-3203(95)00171-9

URL : http://cassius.ee.usyd.edu.au/~adrianw/pr1.ps.gz

L. Alvarez, F. Guichard, P. L. Lions, and J. M. , Morel: Axioms and Fundamental Equations of Images Processing, Archive for Rational Mechanics and Analysis, pp.199-257, 1993.

J. Weickert, a review of nonlinear diffusion filtering, In Scale-Space Theory in Computer Vision, Lecture Notes in Computer Science, vol.1252, 1997.

J. Weickert, Anisotropic Diffusion in Image Processing, 1998.

L. Alvarez, F. Guichard, P. L. Lions, and J. M. , Morel: Axioms and Fundamental Equations of Images Processing, Archive for Rational Mechanics and Analysis, pp.199-257, 1993.

A. Tikhonov and V. , Arsenin: Solution of Ill-Posed Problems, 1977.

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.2553

P. Perona, T. Shiota, and J. Malik, Anisotropic Diffusion Geometry-driven diffusion in computer vision, Dordrecht : Kluwer Academic, pp.229-254, 1994.

F. Catté, J. M. Morel, P. L. Lions, and T. , Image Selective Smoothing and Edge Detection by Nonlinear Diffusion, SIAM Journal on Numerical Analysis, vol.29, issue.1, pp.182-193, 1992.
DOI : 10.1137/0729012

J. Weickert, Scale-space properties of nonlinear diffusion filtering with a diffusion tensor, 1994.

J. Weickert, Anisotropic Diffusion in Image Processing, 1998.

J. Weickert, Coherence-enhancing diffusion of colour images, the 7th National Symposium on Pattern Recognition and Image Analysis, 1997.
DOI : 10.1016/S0262-8856(98)00102-4

N. Sochen, R. Kimmel, and R. Malladi, A geometrical framework for low level vision, IEEE Transaction on Image Processing, Special Issue on PDE based Image Processing, vol.7, issue.3, p.310318, 1998.

R. Kimmel, R. Malladi, and N. , Sochen : Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images, International Journal of Computer Vision, vol.39, issue.2, pp.111-129, 2000.
DOI : 10.1023/A:1008171026419

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.7155

D. Tschumperlé and R. , Deriche : Vector-Valued image regularisation with PDE's: A common framework for different applications, IEEE transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.4, 2005.

H. S. Baird, The state of the art of document image degradation modeling, in book, Digital Document Processing Advances in Pattern Recognition, pp.261-279, 2007.

E. H. Smith and T. Andersen, Text degradations and OCR training, Eighth International Conference on Document Analysis and Recognition (ICDAR'05), pp.834-838, 2005.
DOI : 10.1109/ICDAR.2005.226

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.486.6429

C. Hal and E. H. , Smith : Human Image Preference and Document Degradation Models, International Conference on Document Analysis and Recognition, 2007.

F. Drira and H. Lebourgeois, Emptoz : Document images restoration by a new tensor based diffusion process: Application to the recognition of old printed documents, 10th International Conference on Document Analysis and Recognition (ICDAR), pp.321-325, 2009.

A. Epitomy, T. English-history, and . May, Printed for N. Boddington at the Golden Ball in Duck lane, 1690, University of Michigan, digitized 5 june 2007, http://books.google.fr/books?id=kSE2AAAAMAAJ 62. A vindication of the truth of Christian religion: against the objections of all modern opposers, 1694.