title: Image denoising in mixed Poisson-Gaussian noise.
abstract: 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.
authors.affiliation: Biomedical Imaging Group (BIG), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. florian.luisier@a3.epfl.ch
authors.forename: Florian
authors.initials: F
authors.lastname: Luisier
authors.forename: Thierry
authors.initials: T
authors.lastname: Blu
authors.forename: Michael
authors.initials: M
authors.lastname: Unser
mesh_terms: D000465:Algorithms; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008856:Microscopy, Fluorescence; D015233:Models, Statistical; D016081:Moon; D016011:Normal Distribution; D016012:Poisson Distribution; D014026:Nicotiana / Q000166:cytology