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

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 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.
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Camille Sutour, Charles-Alban Deledalle, Jean-François Aujol. Estimation of the noise level function based on a non-parametric detection of homogeneous image regions. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2015, ⟨10.1137/15M1012682⟩. ⟨hal-01138809v3⟩

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