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When processing a signal or picture by deconvolution, any additional a priori information is of prime interest since it can potentially lead to an improvement in results and to superresolution. In this framework, the positivity of the unknown signal is a current situation (each time this unknown is an intensity, a probability distribution, a histogram, etc.) but it involves a nonlinear constraint which is difficult to take into account. In this paper we state the problem in terms of a quadratic programming problem with positivity constraints and we propose a new algorithm derived from a conjugate gradient method, especially suited to this particular situation. It leads to a low cost solution. We then present experimental results on two-dimensional signals emphasizing relevant superresolution.