Geometric and level set tomography using ensemble Kalman inversion

Hierarchical Bayesian level set inversion

A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data

Abstract. A level-set based approach for the determination of a piecewise constant density function from data of its Radon transformat is presented. Simultaneously, a segmentation of the reconstructed density is obtained. The segmenting contour and the corresponding density are found as minimizers of a Mumford-Shah like functional over the set of admissible contours and — for a fixed contour — ...

Inversion of spherical means using geometric inversion and Radon transforms

We consider the problem of reconstmcting a continuous function on R" from certain values of its spherical means. A novel aspect of our approach is the use of geometric inversion to recast the inverse spherical mean problem as an inverse Radon transform problem. W define WO spherical mean inverse problems the entire problem and the causal problem. We then present a dual filtered backprojection a...

Morphing Ensemble Kalman Filters

A new type of ensemble filter is proposed, which combines an ensemble Kalman filter (EnKF) with the ideas of morphing and registration from image processing. This results in filters suitable for nonlinear problems whose solutions exhibit moving coherent features, such as thin interfaces in wildfire modeling. The ensemble members are represented as the composition of one common state with a spat...

Level Set Method for Positron Emission Tomography

In positron emission tomography (PET), a radioactive compound is injected into the body to promote a tissue-dependent emission rate. Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate. In this paper, we combine the EM algorithm with a leve...