Collaborative Computational Project in Positron Emission Tomography
and Magnetic Resonance imaging

Synergistic Symposium 2019 Machine Learning

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Markus Haltmeier Neural networks, data consistency and regularization in inverse problems
The solution of inverse problems requires regularization methods accounting for instability and non-uniqueness. Classical solution approaches include direct, iterative and variational regularization methods. Recently, deep learning and neural network based algorithms appeared as new paradigm for solving inverse problems. In this talk we propose neural network based approaches enforcing data consistency and stability that are shown to yield regularization methods. We present a convergence analysis, derive convergence rates, and propose possible training strategies for the proposed neural network based methods.
Andreas Maier Image reconstruction using learning with known operators
We describe an approach for incorporating prior knowledge into machine learning algorithms. We aim at applications in physics and signal processing in which we know that certain operations must be embedded into the algorithm. Any operation that allows computation of a gradient or sub-gradient towards its inputs is suited for our framework. We derive a maximal error bound for deep nets that demonstrates that inclusion of prior knowledge results in its reduction. Furthermore, we also show experimentally that known operators reduce the number of free parameters. We apply this approach to various tasks ranging from CT image reconstruction over vessel segmentation to the derivation of previously unknown imaging algorithms. As such the concept is widely applicable for many researchers in physics, imaging, and signal processing. We assume that our analysis will support further investigation of known operators in other fields of physics, imaging, and signal processing.
Claudia Prieto High‐dimensionality patch‐based reconstruction for accelerated multi‐contrast MRI
In MRI, multiple contrasts are exploited to extract clinically relevant tissue parameters and pathological tissue changes. These multiple contrasts are achieved using different imaging sequences and preparation pulses. Multi‐contrast acquisitions also find important applications in parameter mapping (e.g., T1 and T2 mapping) and magnetic resonance fingerprinting (MRF). However, these acquisitions lead to long scan times because multiple images with different contrasts need to be acquired, making parameter imaging more sensitive to physiological motion. Here we describe a new high‐dimensionality undersampled patch‐based reconstruction (HD‐PROST) for highly accelerated 2D and 3D multi‐contrast MRI. HD-PROST jointly reconstructs multi-contrast MR images by exploiting the highly redundant information, on a local and non-local scale, and the strong correlation shared between the multiple contrast images. This is achieved by enforcing multi-dimensional low-rank in the undersampled images.