We propose a new algorithm for restoring quantum limited images. The algorithm is based on projection methods but uses constraint sets in which set membership is based on probabilistic measures. Such constraints can be regarded as soft, as opposed to hard constraints in which less latitude is given in defining set membership. We show that the restoration of quantum- limited images has certain similarities to estimating a probability density function. We apply the algorithm to a widely used image phantom and demonstrate that the processed image features less noise without blurred edges.
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