Image restoration with Poisson–Gaussian mixed noise

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This study focuses on the image denoising and deconvolution problem in case of mixed Gaussian–Poisson noise. By using a maximum a posteriori estimator, we derive a new variational formulation whose minimisation provides the desired restored image. The new functional is composed of the total variation (TV) regularisation term, the Kullback–Leibler divergence term for Poisson noise and the norm fidelity term for Gaussian noise. We consider a dual formulation for the TV term, thus changing the minimisation into a minimax problem. A fast iterative algorithm is derived by using the proximal point method to compute the saddle point of the minimax problem. We show the capability of our model both on synthetic examples and on real images of low-count fluorescence microscopy.