Improved time series reconstruction for dynamic magnetic resonance imaging

Magnetic resonance imaging (MRI) is a noninvasive imaging modality. It does not use ionizing radiation, unlike computerized tomography (CT). Instead, MRI utilizes the magnetic resonance phenomenon and operates at the wavelengths of radio waves. MRI physics includes many parameters that are easy to manipulate. Therefore, MRI also provides a wealth of contrast mechanisms. Over the last decades, researchers have come very close to optimizing MRI hardware, and signal generation and acquisition strategies. This has opened new avenues in diagnostic medicine. The main challenge of MRI seems to be its inherently slow data acquisition. Due to physical and physiological limits on the acquisition side, acceleration algorithms in the post-processing step have become increasingly popular over the last few years. An exciting opportunity for MRI is to utilize it not only in diagnosis, but also as a tool during therapy, owing to its noninvasive nature. Such image guided therapy applications are again hampered by imaging speed and real-time reconstruction limitations.;In this thesis, I use the statistical filtering framework to reconstruct undersampled dynamic MRI acquisitions. This approach tracks the statistics of the underlying system to infer the contributions due to aliasing. While the causality of the Kalman filter makes it a suitable candidate for real-time applications, it can be many orders of magnitude slower than the demand of real-time reconstruction, depending on the sampling pattern. I present a diagonal approximation of the Kalman filter for a large class of linear dynamical systems to arrive at an algorithm that is truly suitable for real-time MRI. Moreover, incoherent sampling can be useful in this linear filtering framework by providing incoherent aliasing artifacts.;Acquisition and system identification strategies are presented to arrive at a practical method. The resulting algorithm can be auto-calibrating without collecting extra samples. I applied the algorithm to dynamic cardiac imaging and performed off-line reconstructions. It is shown to track both small variations and unexpected large variations, such as patient motion or changing of the imaging plane. Improvements in reconstruction quality over the sliding window algorithm are reported in typical real-time scenarios.