Image Restoration with Mixed or Unknown Noises

This paper proposes a simple model for image restoration with mixed or unknown noises. It can handle image restoration without assuming any prior knowledge of the noise distribution. It is particularly useful for solving real-life image restoration problems, since under various constraints, images are always degraded with mixed noise and it is impossible to determine what type of noise is involved. The proposed model can remove mixed-type noises as well as unknown noises and at the same time also works comparably well against the model whose data fitting term is designed for a specific given noise type. While most of the existing methods for image restoration are designed specifically for a given type of noise, ours appears to be the first universal model for handling image restoration with various mixed noises and unknown noises. Extensive simulations on synthetic data show that our method is effective and robust in restoring images contaminated by additive Gaussian noise, Poisson noise, random-valued im...

[1]  Zuowei Shen.  Affine systems in L 2 ( IR d ) : the analysis of the analysis operator , 1995 .

[2]  Jian-Feng Cai,et al.  Split Bregman Methods and Frame Based Image Restoration , 2009, Multiscale Model. Simul..

[3]  John Darzentas,et al.  Problem Complexity and Method Efficiency in Optimization , 1983 .

[4]  Nahum Kiryati,et al.  Image Deblurring in the Presence of Salt-and-Pepper Noise , 2005, Scale-Space.

[5]  Nahum Kiryati,et al.  Image Deblurring in the Presence of Impulsive Noise , 2006, International Journal of Computer Vision.

[6]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..

[7]  F. J. Anscombe,et al.  THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA , 1948 .

[8]  R. Glowinski,et al.  Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[9]  R. Rockafellar.  Monotone Operators and the Proximal Point Algorithm , 1976 .

[10]  Zhang Gong,et al.  Wavelet Frame Based Blind Image Inpainting , 2013 .

[11]  Zuowei Shen.  Wavelet Frames and Image Restorations , 2011 .

[12]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[13]  Hyenkyun Woo,et al.  A New Multiplicative Denoising Variational Model Based on $m$th Root Transformation , 2012, IEEE Transactions on Image Processing.

[14]  Gabriele Steidl,et al.  Deblurring Poissonian images by split Bregman techniques , 2010, J. Vis. Commun. Image Represent..

[15]  R. Tyrrell Rockafellar,et al.  Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming , 1976, Math. Oper. Res..

[16]  I. Daubechies,et al.  Framelets: MRA-based constructions of wavelet frames☆☆☆ , 2003 .

[17]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[18]  Jian-Feng Cai,et al.  Linearized Bregman Iterations for Frame-Based Image Deblurring , 2009, SIAM J. Imaging Sci..

[19]  Bin Dong,et al.  MRA-based wavelet frames and applications , 2013 .

[20]  T. Chan,et al.  DENOISING NATURAL COLOR PHOTOS IN DIGITAL PHOTOGRAPHY , 2022 .

[21]  Zuowei Shen,et al.  Robust video denoising using low rank matrix completion , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[22]  Zuowei Shen,et al.  WAVELET FRAME BASED IMAGE RESTORATION WITH MISSING / DAMAGED PIXELS , 2010 .

[23]  Fionn Murtagh,et al.  Image restoration with noise suppression using a multiresolution support. , 1995 .

[24]  S. Osher,et al.  Image restoration: Total variation, wavelet frames, and beyond , 2012 .

[25]  Thomas J. Asaki,et al.  A Variational Approach to Reconstructing Images Corrupted by Poisson Noise , 2007, Journal of Mathematical Imaging and Vision.

[26]  Thierry Blu,et al.  Image Denoising in Mixed Poisson–Gaussian Noise , 2011, IEEE Transactions on Image Processing.

[27]  Raymond H. Chan,et al.  A Detection Statistic for Random-Valued Impulse Noise , 2007, IEEE Transactions on Image Processing.

[28]  G. Aubert,et al.  A VARIATIONAL APPROACH TO REMOVE MULTIPLICATIVE NOISE , 2006 .

[29]  Kim-Chuan Toh,et al.  An Accelerated Proximal Gradient Algorithm for Frame-Based Image Restoration via the Balanced Approach , 2011, SIAM J. Imaging Sci..

[30]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

[31]  Jianing Shi,et al.  A Nonlinear Inverse Scale Space Method for a Convex Multiplicative Noise Model , 2008, SIAM J. Imaging Sci..

[32]  H. Wu,et al.  Adaptive impulse detection using center-weighted median filters , 2001, IEEE Signal Processing Letters.

[33]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[34]  A. Ron,et al.  Affine Systems inL2(Rd): The Analysis of the Analysis Operator , 1997 .

[35]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[36]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[37]  Gabriele Steidl,et al.  Removing Multiplicative Noise by Douglas-Rachford Splitting Methods , 2010, Journal of Mathematical Imaging and Vision.