Stochastic models for generic images
Quarterly of Applied Mathematics
Limits on Super-Resolution and How to Break Them
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Probabilistic Multi-scale Model for Contour Completion Based on Image Statistics
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
The Nonlinear Statistics of High-Contrast Patches in Natural Images
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Fields of Experts: A Framework for Learning Image Priors
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
IEEE Transactions on Image Processing
Natural image denoising: Optimality and inherent bounds
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Internal statistics of a single natural image
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Building and Using a Database of One Trillion Natural-Image Patches
IEEE Computer Graphics and Applications
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Optimal Spatial Adaptation for Patch-Based Image Denoising
IEEE Transactions on Image Processing
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
From learning models of natural image patches to whole image restoration
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
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Image restoration tasks are ill-posed problems, typically solved with priors. Since the optimal prior is the exact unknown density of natural images, actual priors are only approximate and typically restricted to small patches. This raises several questions: How much may we hope to improve current restoration results with future sophisticated algorithms? And more fundamentally, even with perfect knowledge of natural image statistics, what is the inherent ambiguity of the problem? In addition, since most current methods are limited to finite support patches or kernels, what is the relation between the patch complexity of natural images, patch size, and restoration errors? Focusing on image denoising, we make several contributions. First, in light of computational constraints, we study the relation between denoising gain and sample size requirements in a non parametric approach. We present a law of diminishing return, namely that with increasing patch size, rare patches not only require a much larger dataset, but also gain little from it. This result suggests novel adaptive variable-sized patch schemes for denoising. Second, we study absolute denoising limits, regardless of the algorithm used, and the converge rate to them as a function of patch size. Scale invariance of natural images plays a key role here and implies both a strictly positive lower bound on denoising and a power law convergence. Extrapolating this parametric law gives a ballpark estimate of the best achievable denoising, suggesting that some improvement, although modest, is still possible.