Abstract

Balanced steady-state free precession (bSSFP) is a fast, SNR-efficient magnetic resonance (MR) imaging sequence suffering from dark banding artifacts due to its off-resonance dependence. These banding artifacts are difficult to mitigate at high field strengths and in the presence of metallic implants. Recent developments in parametric modelling of bSSFP have led to advances in banding removal and parameter estimation using multiple phase-cycled bSSFP. With increasing number of coils in receivers, more storage and processing is required. Coil combination is used to reduce dimensionality of these datasets which otherwise might be prohibitively large or computationally intractable for clinical applications. However, our recent work demonstrates that some combination methods are problematic in conjunction with elliptical phase-cycled bSSFP.This thesis will present a method for phase estimation of coil-combined multiple phase-cycled bSSFP to reduce storage and computational requirements for elliptical models. This method is general and works across many coil combination techniques popular in MR reconstruction including the geometric coil combine and adaptive coil combine algorithms. A viable phase estimate for the sum-of-squares is also demonstrated for computationally efficient dimension reduction. Simulations, phantom experiments, and in vivo MR imaging is performed to validate the proposed phase estimates.Compressed sensing (CS) is an increasingly important acquisition and reconstruction framework. CS MR allows for reconstruction of datasets sampled well-under the Nyquist rate and its application is natural in MR where images are often sparse under common linear transforms. An extension of this framework is the ordering problem for CS, first introduced in 2008. Although the assumption is made in CS that images are sparse in some specified transform domain, it might not be maximally sparse. For example, a signal ordered such that it is monotonic is maximally sparse in the finite differences domain. Knowledge of the correct ordering of an image's pixels can lead to much more sparse and powerful regularizers for the CS inverse problem. However, this problem has met with little interest due to the strong dependence on initial image estimates.This thesis will also present an algorithm for estimating the optimal order of a signal such that it is maximally sparse under an arbitrary linear transformation without relying on any prior image estimate. The algorithm is combinatoric in nature and feasible for small signals of interest such as T1 mapping time curves. Proof of concept simulations are performed that validate performance of the algorithm. Computationally feasible modifications for in vivo cardiac T1 mapping are also demonstrated.

Degree

College and Department

Ira A. Fulton College of Engineering and Technology; Electrical and Computer Engineering

Rights

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