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.

performance analysis of maximum likehood methods for nonnegative image deconvolution / P., Favati; Lotti, Grazia; O., Menchi; F., Romani. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 26:(2010). [10.1088/0266-5611/26/8/085013]

performance analysis of maximum likehood methods for nonnegative image deconvolution

LOTTI, Grazia;
2010-01-01

Abstract

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.
2010
performance analysis of maximum likehood methods for nonnegative image deconvolution / P., Favati; Lotti, Grazia; O., Menchi; F., Romani. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 26:(2010). [10.1088/0266-5611/26/8/085013]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2310088
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