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“New Theory and Methods for Accelerated MRI Reconstruction”
by Rodrigo A. Lobos
December 2022
Magnetic Resonance Imaging (MRI) is a safe, versatile, and noninvasive imaging modality that has revolutionized medicine by providing high-quality images of living tissue. Even though MRI technology has been constantly evolving since its origins in the 1970's, the time needed to acquire MRI data can still be restrictively long in real clinical applications. This has limited MRI from reaching its full potential, reason why constant efforts have been made in order to accelerate the data-acquisition process. Most of the adopted approaches to reduce the data-acquisition time involve the individual or combined use of advanced hardware and partial data-acquisition, however, conventional approaches based on these principles can be subject to negative effects in the signal-to-noise ratio, resolution, and/or the presence of undesired artifacts. In this study we propose new computational imaging methods which are able to successfully reconstruct partially acquired data obtained using advanced MRI hardware. Additionally, in this study we propose powerful computational techniques which allow dramatic improvements in computational efficiency when performing the reconstruction task.
In the first part of this study we propose reconstruction methods for partially acquired data which are able to automatically identify multiple linear predictability relationships present in the MRI data. For this purpose we rely on modern structured low-rank modeling theory and advanced optimization techniques. Based on these tools, we make the novel observation that reference data can be used to learn additional linear predictability relationships which considerably improve reconstruction performance in challenging scenarios. For instance, we show that linear relationships learned from reference data allow the reconstruction of highly accelerated data acquired using an undersampling scheme with a uniform structure. Notably, we show that these linear predictability relationships can be learned even in cases where the reference data are not pristine.
In the second part of this study we propose computational techniques in order to improve the efficiency of MRI reconstruction methods. We show that reconstruction methods which are based on the linearly predictable structure of the MRI data can be significantly enhanced in terms of computational complexity by a simple modification in the model used for prediction. Specifically, we show that a missing sample can be predicted using an ellipsoidal neighborhood of samples instead of a rectangular neighborhood of samples, which allows important improvements in computational time and memory usage with negligible effects on performance.
Finally, we study how to improve the efficiency of parallel imaging sensitivity map estimation methods. An accurate estimation of sensitivity maps is a fundamental piece in many modern parallel imaging MRI reconstruction methods, which should also be performed efficiently in order to reduce the overall reconstruction time. In this study we provide a novel theoretical description of the sensitivity map estimation problem by leveraging on the linearly predictable structure of the MRI data. Then, relying on these theoretical results, we propose a powerful set of computational techniques which allow massive improvements in computational complexity when integrated to sensitivity map estimation methods based on subspaces. We show that widely used estimation methods can achieve approximately 100-fold acceleration in computational time and dramatic savings in memory usage without sacrificing estimation accuracy. Remarkably, each of the proposed computational techniques can also be used individually to improve the efficiency of methods in other signal processing applications beyond MRI.