NDLI: Estimation of the Noise Level Function Based on a Nonparametric Detection of Homogeneous Image Regions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Deledalle, Charles-Alban Sutour, Camille Aujol, Jean-François
Copyright Year	2015
Abstract	We propose a two-step algorithm that automatically estimates the noise level function of stationary noise from a single image, i.e., the noise variance as a function of the image intensity. First, the image is divided into small square regions and a nonparametric test is applied to decide whether each region is homogeneous or not. Based on Kendall's $\tau$ coefficient (a rank-based measure of correlation), this detector has a nondetection rate independent of the unknown distribution of the noise, provided that it is at least spatially uncorrelated. Moreover, we prove, on a toy example, that its overall detection error vanishes with respect to the region size as soon as the signal to noise ratio level is nonzero. Once homogeneous regions are detected, the noise level function is estimated as a second order polynomial minimizing the $\ell^1$ error on the statistics of these regions. Numerical experiments show the efficiency of the proposed approach in estimating the noise level function, with a relative error under 10% obtained on a large data set. We illustrate the interest of the approach for an image denoising application.
Starting Page	2622
Ending Page	2661
Page Count	40
File Format	PDF
DOI	10.1137/15M1012682
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	4
Volume Number	8
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-11-17
Access Restriction	Subscribed
Subject Keyword	Image analysis Image processing noise level estimation least absolute deviation signal-dependent noise nonparametric detection
Content Type	Text
Resource Type	Article

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