Prof. Dr. Gerlind Plonka-Hoch
Professor for Applied Mathematics, University of Göttingen
The Multichannel Blind Deconvolution Problem in Parallel MRI
One of the biggest innovations in magnetic resonance imaging (MRI) within the last years was the concept of parallel MRI. In this setting, the use of multiple receiver coils allows the reconstruction of high-resolution images from undersampled Fourier data such that the acquisition time can be substantially reduced. Mathematically, the parallel MRI reconstruction problem can be seen as a multi-channel blind deconvolution problem, where the coil sensitivity functions and the magnetization image have to be recovered simultaneously from the acquired data.
In this talk, we will give a short survey on the mathematical background of some existing reconstruction methods in parallel MRI so far, including GRAPPA, SPIRiT, and ESPIRiT.
Further, we propose the MOCCA algorithm to recover the coil sensitivities and the magnetization image from incomplete Fourier measurements. Our approach is based on a parameter model for the coil sensitivities using bivariate trigonometric polynomials of small degree.
The derived MOCCA algorithm provides perfect reconstruction results if the model assumptions are satisfied. Moreover, it has a low computational complexity and fits real MRI data sufficiently well such that it is applicable in practice.
The results presented in this talk have been obtained jointly with Yannick Riebe and Benjamin Kocur.
Prof. Dr. Michael Unser
Biomedical Imaging Group, Ecole Polytechnique Fédérale de Lausanne (EPFL)
Prof. Dr. Moritz Zaiss
Professor of Multimodal Imaging in Clinical Research, Institute of Neuroradiology, University Hospital Erlangen, Friedrich-Alexander University Erlangen–Nuremberg (FAU)
