Nonlinear Poisson Maximum Likelihood Sample Clauses

Nonlinear Poisson Maximum Likelihood. Another mathematical framework common to image processing applications is a Poisson-based model, in which the data is assumed to be a realization of a Poisson random variable. Tomographic imaging is a classic example of this model. The observed data is based on counts, e.g. photon counts, and can be represented as b = Υ[Ax true] + ε , (1.5) where x true contains voxel values for the true 3D volume, A ∈ Rm×n is a discrete representation of a ray trace operation, Υ[·] models a nonlinear transmission tomography process, and ε is additive noise (assumed to have a Poisson distribution). Given the observed data and information regarding the tomographic process, the goal is to compute an approximation of x true that likely produced the observed data b. To solve this problem, the Pois- son distribution is used to formulate the likelihood function, p(b, x), and standard optimization methods are implemented to maximize the likelihood function. That is, we consider the following problem:
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