Rician Noise Removal via a Learned Dictionary

This paper proposes a new effective model for denoising images with Rician noise. The sparse representations of images have been shown to be efficient approaches for image processing. Inspired by this, we learn a dictionary from the noisy image and then combine the MAP model with it for Rician noise removal. For solving the proposed model, the primal-dual algorithm is applied and its convergence is studied. The computational results show that the proposed method is promising in restoring images with Rician noise.

[1]  Hyenkyun Woo,et al.  Two-Level Convex Relaxed Variational Model for Multiplicative Denoising , 2013, SIAM J. Imaging Sci..

[2]  Jean-Christophe Pesquet,et al.  Playing with Duality , 2015 .

[3]  Nikos Komodakis,et al.  Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems , 2014, IEEE Signal Process. Mag..

[4]  Jian Lu,et al.  A framelet algorithm for de-blurring images corrupted by multiplicative noise , 2018, Applied Mathematical Modelling.

[5]  C. Micchelli,et al.  Proximity algorithms for image models: denoising , 2011 .

[6]  Robert D. Nowak,et al.  Wavelet-based Rician noise removal for magnetic resonance imaging , 1999, IEEE Trans. Image Process..

[7]  Lixin Shen,et al.  Multiplicative noise removal in imaging: An exp-model and its fixed-point proximity algorithm , 2016 .

[8]  Tieyong Zeng,et al.  Poisson noise removal via learned dictionary , 2010, 2010 IEEE International Conference on Image Processing.

[9]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[11]  Yiqiu Dong,et al.  An Efficient Primal-Dual Method for L1TV Image Restoration , 2009, SIAM J. Imaging Sci..

[12]  Dong Liang,et al.  Adaptive Dictionary Learning in Sparse Gradient Domain for Image Recovery , 2013, IEEE Transactions on Image Processing.

[13]  Guido Gerig,et al.  Nonlinear anisotropic filtering of MRI data , 1992, IEEE Trans. Medical Imaging.

[14]  Jian Lu,et al.  Huber Fractal Image Coding Based on a Fitting Plane , 2013, IEEE Transactions on Image Processing.

[15]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[16]  Jian Yu,et al.  A Dictionary Learning Approach for Poisson Image Deblurring , 2013, IEEE Transactions on Medical Imaging.

[17]  Haimiao Zhang,et al.  Wavelet frame based Poisson noise removal and image deblurring , 2017, Signal Process..

[18]  Xiaoping Yang,et al.  A Variational Model to Remove the Multiplicative Noise in Ultrasound Images , 2010, Journal of Mathematical Imaging and Vision.

[19]  Gilles Aubert,et al.  A Variational Approach to Removing Multiplicative Noise , 2008, SIAM J. Appl. Math..

[20]  Tieyong Zeng,et al.  A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise , 2013, SIAM J. Imaging Sci..

[21]  Pascal Getreuer,et al.  A Variational Model for the Restoration of MR Images Corrupted by Blur and Rician Noise , 2011, ISVC.

[22]  Jian-Feng Cai,et al.  Image restoration: A wavelet frame based model for piecewise smooth functions and beyond , 2016 .

[23]  Emanuel A. P. Habets,et al.  Parametric Spatial Sound Processing: A flexible and efficient solution to sound scene acquisition, modification, and reproduction , 2015, IEEE Signal Processing Magazine.

[24]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[25]  Pierrick Coupé,et al.  Rician Noise Removal by Non-Local Means Filtering for Low Signal-to-Noise Ratio MRI: Applications to DT-MRI , 2008, MICCAI.

[26]  José V. Manjón,et al.  MRI denoising using Non-Local Means , 2008, Medical Image Anal..

[27]  F. B. Introduction to Bessel Functions , 1939, Nature.

[28]  A. Hero,et al.  A Fast Spectral Method for Active 3D Shape Reconstruction , 2004 .

[29]  Tony F. Chan,et al.  A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science , 2010, SIAM J. Imaging Sci..

[30]  Yuhao Wang,et al.  A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction , 2016, Int. J. Biomed. Imaging.

[31]  Michael K. Ng,et al.  A New Total Variation Method for Multiplicative Noise Removal , 2009, SIAM J. Imaging Sci..

[32]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[33]  Michael K. Ng,et al.  Multiplicative Noise Removal via a Learned Dictionary , 2012, IEEE Transactions on Image Processing.

[34]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[35]  Alessandro Foi,et al.  Noise estimation and removal in MR imaging: The variance-stabilization approach , 2011, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[36]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[37]  Liyuan Chen,et al.  A Convex Variational Model for Restoring Blurred Images with Large Rician Noise , 2014, Journal of Mathematical Imaging and Vision.

[38]  Lixin Shen,et al.  Proximity algorithms for the L1/TV image denoising model , 2011, Advances in Computational Mathematics.

[39]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[40]  Dong Liang,et al.  Highly Undersampled Magnetic Resonance Image Reconstruction Using Two-Level Bregman Method With Dictionary Updating , 2013, IEEE Transactions on Medical Imaging.

[41]  Raymond H. Chan,et al.  A Multiplicative Iterative Algorithm for Box-Constrained Penalized Likelihood Image Restoration , 2012, IEEE Transactions on Image Processing.

[42]  Lixin Shen,et al.  A new total variation model for restoring blurred and speckle noisy images , 2017, Int. J. Wavelets Multiresolution Inf. Process..

[43]  Pierrick Coupé,et al.  Non-Local Means Variants for Denoising of Diffusion-Weighted and Diffusion Tensor MRI , 2007, MICCAI.

[44]  Yuesheng Xu,et al.  Multiplicative noise removal with a sparsity-aware optimization model , 2017 .

[45]  Kevin M. Johnson,et al.  Wavelet packet denoising of magnetic resonance images: Importance of Rician noise at low SNR , 1999, Magnetic resonance in medicine.

[46]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[47]  Lixin Shen,et al.  Fixed-point algorithms for a TVL1 image restoration model , 2018, Int. J. Comput. Math..

[48]  Junfeng Yang,et al.  An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise , 2009, SIAM J. Sci. Comput..