|Stochastic Systems Group|
Doctoral Student, Boston University
Dynamic tomography is a challenging inverse problem arising in various areas, for example, the reconstruction of time varying tracer distributions in nuclear medicine. The main challenges arise due to the sparsity of the projection data and the ill-conditioning of the tomographic operator. We propose a variational framework based on object models to overcome these difficulties. In our framework, each image of the sequence is modeled as consisting of an object region and a background region. The boundary of the object region is represented as the zero level set of a function. The dynamics of the image sequence is captured through the dynamics of both the object boundary and the intensities. An energy function is then constructed as the sum of four terms: a data fidelity term, a spatial object geometry prior term, an object boundary dynamic term based on an affine dynamic model, and a term for intensity dynamics. We then jointly solve for the dynamic object shape and intensities based on the observed set of projections acquired over time by minimizing this energy. An efficient coordinate descent algorithm based on level set methods is developed to solve this optimization problem. Preliminary experimental results both in 3D and 4D will be presented to demonstrate that our approach allows robust reconstruction of dynamic object sequences from limited projection data acquired over time.
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