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Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation. (English) Zbl 1176.68225
Summary: In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is ill-posed, regularization is needed. Regularized Poisson likelihood estimation has been studied extensively by the authors, though a problem of high importance remains: the choice of the regularization parameter. We present three statistically motivated methods for choosing the regularization parameter, and numerical examples are presented to illustrate their effectiveness.

MSC:
68U10Image processing (computing aspects)
35R99Miscellaneous topics involving PDE