External Prior Guided Internal Prior Learning for Real-World Noisy Image Denoising

Most of existing image denoising methods learn image priors from either an external data or the noisy image itself to remove noise. However, priors learned from an external data may not be adaptive to the image to be denoised, while priors learned from the given noisy image may not be accurate due to the interference of corrupted noise. Meanwhile, the noise in real-world noisy images is very complex, which is hard to be described by simple distributions such as Gaussian distribution, making real-world noisy image denoising a very challenging problem. We propose to exploit the information in both external data and the given noisy image, and develop an external prior guided internal prior learning method for real-world noisy image denoising. We first learn external priors from an independent set of clean natural images. With the aid of learned external priors, we then learn internal priors from the given noisy image to refine the prior model. The external and internal priors are formulated as a set of orthogonal dictionaries to efficiently reconstruct the desired image. Extensive experiments are performed on several real-world noisy image datasets. The proposed method demonstrates highly competitive denoising performance, outperforming state-of-the-art denoising methods including those designed for real-world noisy images.

[1]  Adrian Barbu,et al.  Training an Active Random Field for Real-Time Image Denoising , 2009, IEEE Transactions on Image Processing.

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

[3]  Michael J. Black,et al.  Fields of Experts , 2009, International Journal of Computer Vision.

[4]  Takeo Kanade,et al.  Statistical calibration of CCD imaging process , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[5]  Rebecca Willett,et al.  Poisson Noise Reduction with Non-local PCA , 2012, Journal of Mathematical Imaging and Vision.

[6]  Karen O. Egiazarian,et al.  Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-Image Raw-Data , 2008, IEEE Transactions on Image Processing.

[7]  Xinhao Liu,et al.  Single-Image Noise Level Estimation for Blind Denoising , 2013, IEEE Transactions on Image Processing.

[8]  Guillermo Sapiro,et al.  Non-local sparse models for image restoration , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[9]  Karen O. Egiazarian,et al.  Color Image Denoising via Sparse 3D Collaborative Filtering with Grouping Constraint in Luminance-Chrominance Space , 2007, 2007 IEEE International Conference on Image Processing.

[10]  Ke Chen,et al.  Reweighted sparse subspace clustering , 2015, Comput. Vis. Image Underst..

[11]  Lei Zhang,et al.  External Patch Prior Guided Internal Clustering for Image Denoising , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[12]  Javier Portilla,et al.  Full blind denoising through noise covariance estimation using Gaussian scale mixtures in the wavelet domain , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[13]  David Zhang,et al.  Partial Deconvolution With Inaccurate Blur Kernel , 2018, IEEE Transactions on Image Processing.

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

[15]  Enhong Chen,et al.  Image Denoising and Inpainting with Deep Neural Networks , 2012, NIPS.

[16]  Pheng-Ann Heng,et al.  From Noise Modeling to Blind Image Denoising , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[17]  Michael S. Brown,et al.  A Software Platform for Manipulating the Camera Imaging Pipeline , 2016, ECCV.

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

[19]  David Zhang,et al.  Patch Group Based Nonlocal Self-Similarity Prior Learning for Image Denoising , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[20]  David Zhang,et al.  Patch Group Based Bayesian Learning for Blind Image Denoising , 2016, ACCV Workshops.

[21]  Elsa D. Angelini,et al.  An Unbiased Risk Estimator for Image Denoising in the Presence of Mixed Poisson–Gaussian Noise , 2014, IEEE Transactions on Image Processing.

[22]  Yasuyuki Matsushita,et al.  A Holistic Approach to Cross-Channel Image Noise Modeling and Its Application to Image Denoising , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

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

[24]  Tamer F. Rabie,et al.  Robust estimation approach for blind denoising , 2005, IEEE Transactions on Image Processing.

[25]  Jean-Michel Morel,et al.  The Noise Clinic: a Blind Image Denoising Algorithm , 2015, Image Process. Line.

[26]  Stephen Lin,et al.  A New In-Camera Imaging Model for Color Computer Vision and Its Application , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Michal Irani,et al.  Combining the power of Internal and External denoising , 2013, IEEE International Conference on Computational Photography (ICCP).

[28]  Jos M. F. ten Berge,et al.  A generalization of Kristof's theorem on the trace of certain matrix products , 1983 .

[29]  Stefan Roth,et al.  Benchmarking Denoising Algorithms with Real Photographs , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[30]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[31]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[32]  Jean-Michel Morel,et al.  Multiscale Image Blind Denoising , 2015, IEEE Transactions on Image Processing.

[33]  Martin Greiner,et al.  Wavelets , 2018, Complex..

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

[35]  Pierrick Coupé,et al.  Bayesian Non-local Means Filter, Image Redundancy and Adaptive Dictionaries for Noise Removal , 2007, SSVM.

[36]  Mohamed-Jalal Fadili,et al.  Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal , 2008, IEEE Transactions on Image Processing.

[37]  Richard Szeliski,et al.  Automatic Estimation and Removal of Noise from a Single Image , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[38]  R. Vidal A TUTORIAL ON SUBSPACE CLUSTERING , 2010 .

[39]  Lei Zhang,et al.  Nonlocally Centralized Sparse Representation for Image Restoration , 2013, IEEE Transactions on Image Processing.

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

[41]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[42]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[43]  Alessandro Foi,et al.  Optimal Inversion of the Generalized Anscombe Transformation for Poisson-Gaussian Noise , 2013, IEEE Transactions on Image Processing.

[44]  Glenn Healey,et al.  Radiometric CCD camera calibration and noise estimation , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[45]  Kim-Chuan Toh,et al.  Image Restoration with Mixed or Unknown Noises , 2014, Multiscale Model. Simul..

[46]  Guangyong Chen,et al.  An Efficient Statistical Method for Image Noise Level Estimation , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[47]  Wei Yu,et al.  On learning optimized reaction diffusion processes for effective image restoration , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[48]  Jean-Michel Morel,et al.  A Nonlocal Bayesian Image Denoising Algorithm , 2013, SIAM J. Imaging Sci..

[49]  Stefan Roth,et al.  Shrinkage Fields for Effective Image Restoration , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[50]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2002, IEEE Trans. Image Process..

[51]  René Vidal,et al.  Subspace Clustering , 2011, IEEE Signal Processing Magazine.

[52]  W. Kristof,et al.  A theorem on the trace of certain matrix products and some applications , 1970 .

[53]  Truong Q. Nguyen,et al.  Adaptive Image Denoising by Targeted Databases , 2014, IEEE Transactions on Image Processing.

[54]  David Zhang,et al.  Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).

[55]  Bing Li,et al.  Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means , 2014, J. Sci. Comput..

[56]  Jian Yang,et al.  Mixed Noise Removal by Weighted Encoding With Sparse Nonlocal Regularization , 2014, IEEE Transactions on Image Processing.

[57]  Takeo Kanade,et al.  Statistical Calibration of the CCD Imaging Process , 2001, ICCV.

[58]  Stefan Harmeling,et al.  Image denoising: Can plain neural networks compete with BM3D? , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[59]  David B. Dunson,et al.  Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images , 2012, IEEE Transactions on Image Processing.

[60]  Lei Zhang,et al.  Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising , 2016, IEEE Transactions on Image Processing.

[61]  Yair Weiss,et al.  From learning models of natural image patches to whole image restoration , 2011, 2011 International Conference on Computer Vision.

[62]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).