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.

Osteoarthritis is the most common type of arthritis, and is characterized by the loss of articular cartilage in a joint. This eventually leads to painful bone on bone interactions. Since the loss of cartilage is permanent, the main treatment for this disease is pain management until a full joint replacement is needed. To test new potential treatments a consistent way to measure cartilage thickness is needed. The current standard used in the knee to represent cartilage uses joint space width measured from x-rays. This measurement is highly variable, and does not directly show cartilage. Unlike x-rays, magnetic resonance imaging (MRI) can provide direct visualization of soft tissues in the body, like cartilage. One specific MRI method called balanced steady-state free precession (bSSFP) provides useful contrast between cartilage and its surrounding tissues. This allows easy delineation of the cartilage for volume and thickness measurements. Using bSSFP has unique challenges, but can provide quantitative MR tissue parameter information in addition to volume and thickness measurements.Although bSSFP provides useful contrast, it is highly sensitive to variations in the main magnetic field. This results in dark bands of signal null across an image referred to as banding artifacts. There are a few new methods for mitigating this artifact. An analysis of banding artifact reduction methods is presented in this dissertation. The new methods are shown to be better than traditional methods at reducing banding artifact. However, they do not provide as of high signal to noise ratio as traditional methods in most cases. This analysis is helpful in obtaining artifact free images for volume and thickness measurements.Image distortion can be created when there is a magnetic susceptibility mismatch between bordering substances being imaged, like in the sinuses where air and body tissues meet. A map of the main magnetic field variation can be used to fix this distortion in post processing. A novel method for obtaining a map of the main magnetic field variation is developed using bSSFP in this dissertation. In cases where bSSFP contrast is desirable this map can be obtained with no additional scan time.A new way to sift out MR tissue parameters: T2, T1, and M0 is presented in this dissertation using bSSFP. This method obtains biomarkers that can potentially show the presence of Osteoarthritis before cartilage degeneration begins at the same time as anatomical images. Adjunct scans do not need to be run to get these extra parameters saving scan time. Unlike many adjunct scans, it is also resolution matched to the anatomical images.

Magnetic resonance imaging (MRI) is an important medical imaging technique for visualizing soft tissue structures in the body. It has the advantages of being noninvasive and, unlike x-ray, does not rely on ionizing radiation for imaging. In traditional hydrogen-based MRI, the strongest measured signals are generated from the hydrogen nuclei contained in water and fat molecules.Reliable and uniform water fat separation can be used to improve medical diagnosis. In many applications the water component is the primary signal of interest, while the fat component represents a signal which can obscure the underlying pathology or other features of interest. In other applications the fat signal is the signal of interest. There currently exist many techniques for water fat separation. Dixon reconstruction techniques take multiple images acquired at select echo times with specific phase properties. Linear combinations of these images produce separate water and fat images. In MR imaging, images with high signal-to-noise ratio (SNR), that can be generated in a short time, are desired. Balanced steady-state free precession (bSSFP) MRI is a technique capable of producing images with high SNR in a short imaging time but suffers from signal voids or banding artifacts due to magnetic field inhomogeneity and susceptibly variations. These signal voids degrade image quality. Several methods have been developed to remove these banding effects. The simplest methods combine images across multiple bSSFP image acquisitions. This thesis describes a technique in water fat separation I developed which combines the advantages of bSSFP with Dixon reconstruction in order to produce robust water fat decomposition with high SNR in a short imaging time, while simultaneously reducing banding artifacts which traditionally degrade image quality. This algorithm utilizes four phased-cycled bSSFP acquisitions at specific echo times. Phase sensitive post-processing and a field map are used to prepare the data and reduce the effects of field inhomogeneities. Dixon reconstruction is then used to generate separate water and fat images.

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