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Shape-based image reconstruction using linearized deformations. (English) Zbl 1372.35369

Summary: We introduce a reconstruction framework that can account for shape related prior information in imaging-related inverse problems. It is a variational scheme that uses a shape functional, whose definition is based on deformable template machinery from computational anatomy. We prove existence and, as a proof of concept, we apply the proposed shape-based reconstruction to 2D tomography with very sparse and/or highly noisy measurements.

MSC:

35R30 Inverse problems for PDEs
35A15 Variational methods applied to PDEs

Software:

PMTK; ODL
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References:

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