Image Denoising by Random Interpolation Average with Low-Rank Matrix Approximation

With the wide deployment of digital image capturing equipment, the need of denoising to produce a crystal clear image from noisy capture environment has become indispensable. This work presents a novel image denoising method that can tackle both impulsive noise, such as salt and pepper noise (SAPN), and additive white Gaussian noise (AWGN), such as hot carrier noise from CMOS sensor, at the same time. We propose to use low-rank matrix approximation to form the basic denoising framework, as it has the advantage of preserving the spatial integrity of the image. To mitigate the SAPN, the original noise corrupted image is randomly sampled to produce sampled image sets. Low-rank matrix factorization method (LRMF) via alternating minimization denoising method is applied to all sampled images, and the resultant images are fused together via a wavelet fusion with hard threshold denoising. Since the sampled image sets have independent but identical noise property, the wavelet fusion serves as the effective mean to remove the AWGN, while the LRMF method suppress the SAPN. Simulation results are presented which vividly show the denoised images obtained by the proposed method can achieve crystal clear image with strong structural integrity and showing good performance in both subjective and objective metrics.

[1]  Yan Yan,et al.  $L_{1}$ -Norm Low-Rank Matrix Factorization by Variational Bayesian Method , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[2]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

[3]  Anil K. Jain,et al.  Segmentation and Enhancement of Latent Fingerprints: A Coarse to Fine RidgeStructure Dictionary , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Thierry Blu,et al.  SURE-LET for Orthonormal Wavelet-Domain , 2010 .

[5]  Yan Liu,et al.  Weighted Schatten $p$ -Norm Minimization for Image Denoising and Background Subtraction , 2015, IEEE Transactions on Image Processing.

[6]  Michael Elad,et al.  K-SVD dictionary-learning for the analysis sparse model , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[7]  Emmanuel J. Candès,et al.  Matrix Completion With Noise , 2009, Proceedings of the IEEE.

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

[9]  Thomas S. Huang,et al.  Image Super-Resolution Via Sparse Representation , 2010, IEEE Transactions on Image Processing.

[10]  Peyman Milanfar,et al.  A Tour of Modern Image Filtering: New Insights and Methods, Both Practical and Theoretical , 2013, IEEE Signal Processing Magazine.

[11]  Lei Zhang,et al.  Sparsity-based image denoising via dictionary learning and structural clustering , 2011, CVPR 2011.

[12]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[13]  Hing Cheung So,et al.  Outlier-Robust Matrix Completion via $\ell _p$ -Minimization , 2018, IEEE Transactions on Signal Processing.

[14]  Shiqian Ma,et al.  Fixed point and Bregman iterative methods for matrix rank minimization , 2009, Math. Program..

[15]  B. S. Manjunath,et al.  Multi-sensor image fusion using the wavelet transform , 1994, Proceedings of 1st International Conference on Image Processing.

[16]  Yusen Wei,et al.  RANDOM INTERPOLATION AVERAGE FOR ECG SIGNAL DENOISING USING MULTIPLE WAVELET BASES , 2013 .

[17]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[18]  P. Tseng Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization , 2001 .

[19]  Lei Zhang,et al.  Image Restoration: From Sparse and Low-Rank Priors to Deep Priors [Lecture Notes] , 2017, IEEE Signal Processing Magazine.

[20]  Bernard Ghanem,et al.  𝓁0TV: A Sparse Optimization Method for Impulse Noise Image Restoration , 2018, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Cornelia Fermüller,et al.  Robust Wavelet-Based Super-Resolution Reconstruction: Theory and Algorithm , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  M. Omair Ahmad,et al.  Video Denoising Based on Inter-frame Statistical Modeling of Wavelet Coefficients , 2007, IEEE Transactions on Circuits and Systems for Video Technology.

[23]  Liangpei Zhang,et al.  Hyperspectral Image Denoising via Noise-Adjusted Iterative Low-Rank Matrix Approximation , 2015, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[24]  Etienne E. Kerre,et al.  A fuzzy impulse noise detection and reduction method , 2006, IEEE Transactions on Image Processing.

[25]  Michael Elad,et al.  On the Role of Sparse and Redundant Representations in Image Processing , 2010, Proceedings of the IEEE.

[26]  Prateek Jain,et al.  Low-rank matrix completion using alternating minimization , 2012, STOC '13.

[27]  Kannan Ramchandran,et al.  Low-complexity image denoising based on statistical modeling of wavelet coefficients , 1999, IEEE Signal Processing Letters.

[28]  Peyman Milanfar,et al.  Clustering-Based Denoising With Locally Learned Dictionaries , 2009, IEEE Transactions on Image Processing.

[29]  David Suter,et al.  Recovering the missing components in a large noisy low-rank matrix: application to SFM , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  David Gamarnik,et al.  A Note on Alternating Minimization Algorithm for the Matrix Completion Problem , 2016, IEEE Signal Processing Letters.

[31]  Anand Rangarajan,et al.  Image Denoising Using the Higher Order Singular Value Decomposition , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Aggelos K. Katsaggelos,et al.  Digital image restoration , 2012, IEEE Signal Process. Mag..

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

[34]  B. S. Manjunath,et al.  Multisensor Image Fusion Using the Wavelet Transform , 1995, CVGIP Graph. Model. Image Process..

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

[36]  S. Yun,et al.  An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems , 2009 .

[37]  Jian-Feng Cai,et al.  Two-phase approach for deblurring images corrupted by impulse plus gaussian noise , 2008 .

[38]  Ali Mohammad-Djafari,et al.  Introduction to Inverse Problems in Imaging and Vision , 2013 .

[39]  Jian Yu,et al.  Restoration of images corrupted by mixed Gaussian-impulse noise via l1-l0 minimization , 2011, Pattern Recognit..

[40]  Charles Kervrann,et al.  Nonlocal Means and Optimal Weights for Noise Removal , 2017, SIAM J. Imaging Sci..

[41]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[42]  Dacheng Tao,et al.  On the Performance of Manhattan Nonnegative Matrix Factorization , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[43]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[44]  Peyman Milanfar,et al.  Patch-Based Near-Optimal Image Denoising , 2012, IEEE Transactions on Image Processing.

[45]  Michael Elad,et al.  Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model , 2013, IEEE Transactions on Signal Processing.

[46]  Andrew W. Fitzgibbon,et al.  Damped Newton algorithms for matrix factorization with missing data , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[47]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

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

[49]  Dong Wang,et al.  Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[50]  Lei Zhang,et al.  Weighted Nuclear Norm Minimization with Application to Image Denoising , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[51]  Raymond H. Chan,et al.  Fast Two-Phase Image Deblurring Under Impulse Noise , 2009, Journal of Mathematical Imaging and Vision.

[52]  Stefanos Zafeiriou,et al.  Robust Kronecker Component Analysis , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[53]  Karen O. Egiazarian,et al.  Image denoising with block-matching and 3D filtering , 2006, Electronic Imaging.

[54]  Y. Yang,et al.  Random interpolation average for signal denoising , 2010 .