Luisier, F.Blu, T.Unser, M.2011-02-172011-02-172011-02-17201110.1109/TIP.2010.2073477https://infoscience.epfl.ch/handle/20.500.14299/64530WOS:000287400700008We 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.FilterbankGaussian noiseimage denoisingMSE estimationPoisson noisethresholdingunbiased risk estimateWavelet ShrinkageIntensity EstimationRedundant RepresentationsMultiscale ModelsRestorationCurveletsDomainCIBM-SPtext::journal::journal article::research article