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)
Deep-Spline Neural Networks for Stable Image Reconstruction
The two dominant CNN-based paradigms for consistent biomedical image reconstruction are: (i) approaches based on trainable regularizers; and (ii) proximal-gradient-type architectures, such as plug-and-play (PnP) methods, that rely on a learned denoiser. A major challenge in both settings is the control of stability and convergence, which typically requires restrictive conditions such as convexity of the regularizer or nonexpansiveness of the denoiser. While effective from a theoretical standpoint, these constraints may reduce the representational power of the resulting models.
In this work, we propose a framework that increases model flexibility by learning the neuronal activation functions jointly with the network parameters, while maintaining explicit control over their slopes. The activations are parameterized as adaptive linear splines obtained through a second-order total-variation regularization principle. This formulation leads to parsimonious and trainable spline-based neural architectures that can be integrated within stable reconstruction schemes. We demonstrate the practicality of the proposed approach on denoising and biomedical image-reconstruction tasks, where it achieves competitive and robust performance.
Prof. Dr. Moritz Zaiss
Professor of Multimodal Imaging in Clinical Research, Institute of Neuroradiology, University Hospital Erlangen, Friedrich-Alexander University Erlangen–Nuremberg (FAU)
MR-zero: How MR Physicists Move Fast and Break Things
In the MR-zero project [1,2], we approached to reinvent MRI from scratch by treating MR sequence design as a learning-based optimization problem. We formulate an end-to-end differentiable simulation pipeline, given a specific imaging task or even just a target image, the entire chain can be optimized jointly.
In this talk, I will introduce the MR-zero approach and illustrate it with examples: learning MRI from scratch, improving image sharpness in TSE and FLASH MRI, optimizing sequences for imperfect scanner systems, and performing end-to-end quantitative MRI experiments. These results show what becomes possible when we borrow tools from optimization, automatic differentiation, and machine learning and combine it with recent MR physics developments like phase distribution graphs [3].
At the same time, MR-zero is far from an ideal mathematical framework. Many parts of the pipeline and problem formulation are still in progress, and are slow, unstable, approximate, or non-optimal. For this audience, this is exactly the point: the project exposes open problems in inverse problems in MR, differentiable simulation, typical optimization constraints and regularizations, and the translation from continuous models to executable scanner experiments. The talk is both a report and an invitation. I will show what we achieved with out-of-the-box mathematical tools, and where we would benefit from deeper mathematical insight. If you leave thinking, “What are they even doing? This could be done so much better,” then the talk has succeeded.
[1] https://mrsources.github.io/MRzero-Core/
[2] https://doi.org/10.1002/mrm.28727
[3] https://doi.org/10.1002/mrm.30055