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A nonlocal Bayesian image denoising algorithm. (English) Zbl 1279.68331

Summary: Recent state-of-the-art image denoising methods use nonparametric estimation processes for \(8 \times 8\) patches and obtain surprisingly good denoising results. The mathematical and experimental evidence of two recent articles suggests that we might even be close to the best attainable performance in image denoising ever. This suspicion is supported by a remarkable convergence of all analyzed methods. Still more interestingly, most patch-based image denoising methods can be summarized in one paradigm, which unites the transform thresholding method and a Markovian Bayesian estimation. As the present paper shows, this unification is complete when the patch space is assumed to be a Gaussian mixture. Each Gaussian distribution is associated with its orthonormal basis of patch eigenvectors. Thus, transform thresholding (or a Wiener filter) is made on these local orthogonal bases. In this paper a simple patch-based Bayesian method is proposed, which on the one hand keeps most interesting features of former methods, and on the other hand slightly improves the state of the art of color images.

MSC:

68U10 Computing methodologies for image processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
62-04 Software, source code, etc. for problems pertaining to statistics
62C12 Empirical decision procedures; empirical Bayes procedures
62F15 Bayesian inference
62G07 Density estimation
60H40 White noise theory

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