An efficient computational method for total variation-penalized Poisson likelihood estimation
Johnathan M. Bardsley - Department of Mathematical Sciences, University of Montana Missoula, Montana 59812, United States (email)
Approximating non-Gaussian noise processes with Gaussian models is standard in data analysis. This is due in large part to the fact that Gaussian models yield parameter estimation problems of least squares form, which have been extensively studied both from the theoretical and computational points of view. In image processing applications, for example, data is often collected by a CCD camera, in which case the noise is a Guassian/Poisson mixture with the Poisson noise dominating for a sufficiently strong signal. Even so, the standard approach in such cases is to use a Gaussian approximation that leads to a negative-log likelihood function of weighted least squares type.
Keywords: total variation,
nonnegatively constrained optimization, image reconstruction,
Bayesian statistical methods.
Received: February 2007; Revised: January 2008; Available Online: April 2008.
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