Learning Weighted Least Squares Data Term for Poisson Image Deconvolution

Weighted least squares are often used to approximate log-likelihoods when solving inverse problems involving non-Gaussian noise as they are more appealing from an optimization perspective. Although a theoretical expression of the weights can be derived for specific noises, this may become intractable for more general noises. Moreover, such theoretical weights can be detrimental to the efficiency of optimization algorithms. To remedy these issues, we propose in this work to learn the weights from data so as to adapt to any general noise while maintaining the efficiency of optimization. The proposed pipeline combines a weight estimation module with an unrolled optimization algorithm. The weight estimation module and a few parameters of the unrolled algorithm are trained together in an end-to-end manner. We demonstrate the effectiveness of the proposed methodology in the context of Poisson image deconvolution.