Adaptive Regularization Techniques for Image Reconstruction in Accelerated MRI

Magnetic resonance imaging (MRI) is a non-invasive medical imaging modality for the
visualization of soft tissues. Despite the capability of providing high-resolution images,
the difficulties associated with lengthy acquisition time necessitates reconstruction of the
final image from a limited number of k-space samples. The reconstruction procedures can
be either linear methods in k-space or image domain, or non-linear approaches that utilize
the compressed sensing (CS) theory. As all the aforementioned reconstruction procedures
fall under the broad class of ill-posed inverse problems, the effective incorporation of the
prior information, called regularization, is necessary for obtaining stable and meaningful
solutions. However, the accuracy of regularized output depends on the regularization
parameter choice. This thesis outlines methods based on model based optimization
techniques to adaptively estimate the regularization parameters in both spectral and sparse
domains.
The initial part of this thesis addresses the problems related to a single filter calibration in
linear k-space methods due to signal-to-noise (SNR) variation of magnetic resonance
(MR) signal across different k-space locations. The succeeding part of the thesis addresses
the iteratively dependent selection of the regularization parameter value associated with
non-linear cost functions used to obtain optimal solutions in CS formulation. In the final
part of the thesis, parameter selection for continuation is formulated as an optimization
problem, in which the desired solution is computed using an alternating minimization
approach.

PHD THESIS JUNE 2020 INT Dr. JOSEPH SURESH PAUL
Professor
Medical Image Computing and Signal Processing Laboratory
Indian Institute of Information Technology and Management-Kerala
Thiruvananthapuram 695581
Cochin University of Science and Technology