Institut für Mathematik
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Shearlet and Sparse Regularization Techniques for Improved MRE Imaging
PIs: Kutyniok, Fischer, Hege, Sack
Application areas: Cardiovascular, cancer
Modalities: PAT, US, MR
Inverse scattering problems occur in medical imaging in various ways. Of particular importance is the acoustic inverse scattering problem, which models the reconstruction procedure from data generated by, for instance, PAT, US, and elastography. We will introduce a mathematical model for 3D scatterers by accounting for anisotropic features prevalent in biological tissues such as connective tissue fibers, blood vessels, or lactiferous ducts. Given generalized geometrical features of self-similar 3D anisotropic networks in biological tissues, the model will provide an efficient mathematical treatment of highly complex scattering phenomena and enable us to invoke adapted regularization strategies such as the L1-norm of carefully chosen representation systems (e.g. shearlets) capable of sparsifying the model functions. Based on this approach, an optimal – in the sense of approximation accuracy – reconstruction scheme will be developed and analyzed with respect to realistic noise assumptions.