Video Denoising via Empirical Bayesian Estimation of Space-Time Patches

• Published in: Journal of mathematical imaging and vision Vol. 60; no. 1; pp. 70 - 93
• Main Authors: Arias, Pablo, Morel, Jean-Michel
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2018; Springer Nature B.V; Springer Verlag
• Subjects: Applications of Mathematics; Bayesian analysis; Computer Science; Computer Vision and Pattern Recognition; Covariance matrix; Eigenvalues; Engineering Sciences; Estimators; Image Processing; Image Processing and Computer Vision; Mathematical Methods in Physics; Mathematics; Motion simulation; Noise reduction; Numerical Analysis; Patches (structures); Signal and Image processing; Signal,Image and Speech Processing; Spacetime; Statistical analysis; Statistical methods; Empirical Bayes; Video denoising; Wiener filtering; Bayesian methods; Video restoration; Patch-based methods; Covariance matrix estimation
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-017-0742-4

In this paper we present a new patch-based empirical Bayesian video denoising algorithm. The method builds a Bayesian model for each group of similar space-time patches. These patches are not motion-compensated, and therefore avoid the risk of inaccuracies caused by motion estimation errors. The high dimensionality of spatiotemporal patches together with a limited number of available samples poses challenges when estimating the statistics needed for an empirical Bayesian method. We therefore assume that groups of similar patches have a low intrinsic dimensionality, leading to a spiked covariance model . Based on theoretical results about the estimation of spiked covariance matrices, we propose estimators of the eigenvalues of the a priori covariance in high-dimensional spaces as simple corrections of the eigenvalues of the sample covariance matrix. We demonstrate empirically that these estimators lead to better empirical Wiener filters. A comparison on classic benchmark videos demonstrates improved visual quality and an increased PSNR with respect to state-of-the-art video denoising methods.