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Multiscale Variance-Stabilizing Transform for Mixed-Poisson-Gaussian Processes and its Applications in Bioimaging

Fluorescence microscopy images are contaminated by photon and readout noises, and hence can be described by mixed-Poisson-Gaussian (MPG) processes. In this paper, a new variance stabilizing transform (VST) is designed to convert a filtered MPG process into a near Gaussian process with a constant variance. This VST is then combined with the isotropic undecimated wavelet transform leading to a multiscale VST (MS-VST). We demonstrate the usefulness of MS-VST for image denoising and spot detection in fluorescence microscopy. In the first case, we detect significant Gaussianized wavelet coefficients under the control of a false discovery rate. A sparsity-driven iterative scheme is proposed to properly reconstruct the final estimate. In the second case, we show that the MS-VST can also lead to a fluorescent-spot detector, where the false positive rate of the detection in pure noise can be controlled. Experiments show that the MS-VST approach outperforms the generalized Anscombe transform in denoising, and that the detection scheme allows efficient spot extraction from complex background.