SUTOUR, Camille; DELEDALLE, Charles-Alban; AUJOL, Jean-François

doi:10.1137/15M1012682

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SUTOUR, Camille
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]

DELEDALLE, Charles-Alban
Institut de Mathématiques de Bordeaux [IMB]

AUJOL, Jean-François
Institut de Mathématiques de Bordeaux [IMB]

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SIAM Journal on Imaging Sciences. 2015-11-17

Society for Industrial and Applied Mathematics

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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 non-parametric test is applied to decide weather each region is homogeneous or not. Based on Kendall's τ coefficient (a rank-based measure of correlation), this detector has a non-detection rate independent on 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 non-zero. Once homogeneous regions are detected, the noise level function is estimated as a second order polynomial minimizing the ℓ 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.< Réduire

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non-parametric detection

signal-dependent noise

Noise level estimation

least absolute deviation

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Estimation of the noise level function based on a non-parametric detection of homogeneous image regions

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