OptOP
Optimal control for optimal operators
From the mathematical perspective, image reconstruction in MRI is an inverse problem, where the forward operator to invert—determined by the dynamical system associated with the underlying physical model—maps the desired quantities, like an image, to the measurements recorded by the device. In particular, for MRI, a plethora of acquisition strategies are available, each can be seen to correspond to a fixed control of the underlying system and leading to a different forward operator that must be inverted in a regularized fashion. In turn, by switching to an optimal control paradigm for these dynamical systems targeting regularization theory in inverse problems, opportunities arise to develop novel acquisition strategies that are designed towards optimally improving the quality of image reconstruction. Such innovation has far-reaching implications beyond MRI, calling for a general mathematical study of optimal control for optimal operators.
To this end, subproject OptOP investigates optimal control problems involving the control-to-forward-operator map arising in the dynamic measurement setup, with the aim of optimally solving inverse problems. It blends abstract mathematical analysis, data-driven approaches, and algorithmic development in the pursuit of more accurate inversion techniques that are robust to noisy data. The proposed strategies range from optimization involving bilevel control of affine linear forward operators to advanced learning-based reconstruction methods in the context of nonlinear inversion. We will further tackle pivotal MRI applications, with the Bloch equation guiding the optimization of measurement and reconstruction operators, employing the newly-developed techniques and leveraging the results of the other subprojects.
We will work with BiCONTROL and IdCONTROL on analyzing bilevel control and improving parameter identification, collaborate with BiLEARN to integrate motion, develop jointly with PriorLEARN data-driven learned reconstruction methods, enhance the targeted models together with ModLEARN, and link with GenMRI to MR scanner technology.