An Iterative Method for Edge-Preserving MAP Estimation When Data-Noise Is Poisson

In numerous applications of image processing, e.g. astronomical and medical imaging, data-noise is well-modeled by a Poisson distribution. This motivates the use of the negative-log Poisson likelihood function for data fitting. (The fact that application scientists in both astronomical and medical imaging regularly choose this function for data fitting provides further motivation.) However difficulties arise when the negative-log Poisson likelihood is used. Chief among them are the facts that it is non-quadratic and is defined only for vectors with nonnegative values. The nonnegatively constrained, convex optimization problems that arise when the negative-log Poisson likelihood is used are therefore more challenging than when least squares is the fit-to-data function. Edge preserving deblurring and denoising has long been a problem of keen interest in the image processing community. While total variation regularization is the gold standard for such problems, its use yields computat...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Johnathan M. Bardsley, John Goldes
• Keywords: Negative-log Poisson, Negative-log Poisson Likelihood, Regularization Function, SIAMSC 2010