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Image Denoising in Mixed Poisson–Gaussian Noise

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3 Author(s)
Luisier, F. ; Biomed. Imaging Group (BIG), Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland ; Blu, T. ; Unser, M.

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds (LET) that we optimize by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE), derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate). We provide a practical approximation of this theoretical MSE estimate for the tractable optimization of arbitrary transform-domain thresholding. We then propose a pointwise estimator for undecimated filterbank transforms, which consists of subband-adaptive thresholding functions with signal-dependent thresholds that are globally optimized in the image domain. We finally demonstrate the potential of the proposed approach through extensive comparisons with state-of-the-art techniques that are specifically tailored to the estimation of Poisson intensities. We also present denoising results obtained on real images of low-count fluorescence microscopy.

Published in:

Image Processing, IEEE Transactions on  (Volume:20 ,  Issue: 3 )