# A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations

@article{Dup2008API, title={A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations}, author={François-Xavier Dup{\'e} and Mohamed-Jalal Fadili and Jean-Luc Starck}, journal={IEEE Transactions on Image Processing}, year={2008}, volume={18}, pages={310-321} }

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are as follows. First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a nonlinear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the…

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