performance analysis of maximum likehood methods for nonnegative image deconvolution

In many numerical applications, for instance in image deconvolution, the nonnegativity of the computed solution is required. When a prob- lem of deconvolution is formulated in a statistical frame, the recorded image is seen as the realization of a random process, where the nature of the noise is taken into account. This formulation leads to the maximiza- tion of a likelihood function which depends on the statistical property assumed for the noise. In this paper we revisit, under this unifying sta- tistical approach, some iterative methods coupled with suitable strategies for enforcing nonnegativity and other ones which instead naturally embed nonnegativity. For all these methods we carry out a comparative study taking into account several performance indicators. The reconstruction accuracy, the computational cost, the consistency with the discrepancy principle (a common technique for guessing the best regularization pa- rameter) and the sensitivity to this choice are compared in a simulation context, by means of an extensive experimentation on both 1D and 2D problems.