KEYWORDS: Signal to noise ratio, Image restoration, Electron tomography, Reconstruction algorithms, Tomography, Data modeling, Compressed sensing, Mathematical modeling, Statistical modeling
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.
Direct image formation in synthetic aperture radar (SAR) involves processing of data modeled as Fourier coefficients along a polar grid. Often in such data acquisition processes, imperfections in the data cannot simply be modeled as additive or even multiplicative noise errors. In the case of SAR, errors in the data can exist due to imprecise estimation of the round trip wave propagation time, which manifests as phase errors in the Fourier domain. To correct for these errors, we propose a phase correction scheme that relies on both the on smoothness characteristics of the image and the phase corrections associated with neighboring pulses, which are possibly highly correlated due to the nature of the data off setting. Our model takes advantage of these correlations and smoothness characteristics simultaneously for a new autofocusing approach, and our algorithm for the proposed model alternates between approximate image feature and phase correction minimizers to the model.
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