Constrained Magnetic Resonance and Computed Tomographic Imaging: Models and Applications

Abstract

Tomographic imaging systems like CT and MRI allow the visualization of the interior of objects and are invaluable in diverse applications such as medical imaging and security scanning. These systems usually consist of two separate sub-systems: data acquisition and image reconstruction. Traditional imaging usually involves sampling at the Nyquist rate, and places the overwhelming burden of image formation on the data acquisition side. The reconstruction module simply acts as a mapping from the measurement space to image space. Acquiring data at the full sampling rate can be prohibitively expensive in several applications. There is tremendous interest in forming images from subsampled data to improve scanning throughput and reduce scan times. In diagnostic imaging, there are additional motivating factors to lower scan times: reduced patient discomfort, lowered motion sensitivity, and enabling novel imaging applications. Constrained imaging (CI) seeks to form images from subsampled data by enforcing suitable constraints on the images. A major difference from traditional imaging is that CI shifts a significant part of the image formation burden from the data acquisition system to the reconstruction system.

MRI is a valuable tool for diagnostic applications but is popularly used as a qualitative imaging modality. However, MRI can also support the quantification of tissue specific parameters making it valuable for tissue characterization and pathological assessment. The mapping of tissue relaxation parameters like T1 and T2 is an emerging area of interest in quantitative MRI called parameter mapping. Classical parameter mapping experiments are plagued by extremely long scan times due to the need to form images with multiple contrast weightings. Using sub-sampled data for image formation is critical to allow these scans to be performed in a clinically acceptable time. This dissertation studies two different CI models for relaxation mapping. The proposed models seek to improve reconstruction performance by incorporating novel prior information, drawn from clustering/classification models like k-means and block matching, into the reconstruction process. Monte-Carlo simulations are performed to analyze the bias-variance properties of the models and in-vivo results are presented to further demonstrate performance.

X-ray CT plays a major role in baggage scanning for security applications. A major consideration in the operational pipelines for security scanning is the achievable scanning throughput while maintaining the necessary threat detection / false alarm rates. CI is emerging as a viable option to achieve improved throughputs in these applications and we study the performance of two different CI models in this context. While demonstrating high quality image recovery, CI models can be slow (heavy computational requirements) making their translation into real life systems challenging. Models based on deep learning, specifically Convolutional Neural Networks (CNN), have emerged as the state-of-art in several image processing tasks like recognition and classification. CNN based models tend to have remarkably low computational overhead making them valuable in applications that demand near real time processing. We study the performance of two different CNN models for image recovery of subsampled CT data and compare them with the CI models.