A Unified Framework for the Restoration of Images Corrupted by Additive White Noise

We propose a robust variational model for the restoration of images corrupted by blur and the general class of additive white noises. The solution of the non-trivial optimization problem, due to the non-smooth non-convex proposed model, is efficiently obtained by an Alternating Directions Method of Multipliers (ADMM), which in particular reduces the solution to a sequence of convex optimization sub-problems. Numerical results show the potentiality of the proposed model for restoring blurred images corrupted by several kinds of additive white noises.

[1]  R. Chan,et al.  An Adaptive Strategy for the Restoration of Textured Images using Fractional Order Regularization , 2013 .

[2]  Michael Werman,et al.  Probabilistic Analysis of Regularization , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  M. Nikolova.  A Variational Approach to Remove Outliers and Impulse Noise , 2004 .

[4]  Xuecheng Tai,et al.  AUGMENTED LAGRANGIAN METHOD FOR TOTAL VARIATION RESTORATION WITH NON-QUADRATIC FIDELITY , 2011 .

[5]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[6]  Ken D. Sauer,et al.  A generalized Gaussian image model for edge-preserving MAP estimation , 1993, IEEE Trans. Image Process..

[7]  Christian Clason,et al.  L∞ fitting for inverse problems with uniform noise , 2012 .

[8]  Serena Morigi,et al.  Variational Image Restoration with Constraints on Noise Whiteness , 2014, Journal of Mathematical Imaging and Vision.

[9]  Anthony J. Yezzi,et al.  Variational Image Denoising Based on Autocorrelation Whiteness , 2013, SIAM J. Imaging Sci..

[10]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[11]  Tieyong Zeng,et al.  Variational Approach for Restoring Blurred Images with Cauchy Noise , 2015, SIAM J. Imaging Sci..

[12]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

[13]  Jerry D. Gibson,et al.  Handbook of Image and Video Processing , 2000 .

[14]  Serena Morigi,et al.  Image restoration with Poisson–Gaussian mixed noise , 2014, Comput. methods Biomech. Biomed. Eng. Imaging Vis..

[15]  Adi Ben-Israel,et al.  A concentrated Cauchy distribution with finite moments , 2013, Ann. Oper. Res..

[16]  Bernard Widrow,et al.  Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications , 2008 .

[17]  Serena Morigi,et al.  Constrained TV$$_p$$p-$$\ell _2$$ℓ2 Model for Image Restoration , 2015 .