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The potential for Poisson image reconstruction models for electron tomography

Image reconstruction models that deal with Poisson noise have received notable attention for image denoising and deblurring problems. Tomography does not fall into this category, and such methods have yet to be explored for applications such as electron tomography, where the noise is dominated by Poisson noise. In this domain, the use of Poisson models becomes much more challenging, where popular methods such as the Richardson-Lucy algorithm cannot be implemented. The purpose of this article is to provide a survey of Poisson image reconstruction models in the context of tomography, and identify the most successful algorithms and the benefits over the current standard techniques. Methods using both ℓ1 and ℓ2 regularization techniques are investigated, while the data fitting methods include both iteratively reweighted norms and negatively log-likelihood methods derived from the Bayesian formulation. The results of this work indicate a consistent improvement when implementing the appropriate Poisson models.