TU Berlin

Institut für Mathematik

Straße des 17. Juni 136, Room MA 575

10623 Berlin

Telephone: +49 30 3142 5752

Email: stephanw@math.tu-berlin.de

 

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.