The MRI analysis pipeline consists of a data-acquisition stage defined by a protocol, an estimation stage defined by a function, and an analysis stage - normally performed by a radiologist. MRI data is acquired as a 3D or 4D grid of complex-valued measurements. In some protocols more than one set of measurements are fused into a vector of complex values. However, radiologists normally desire a real-valued 3D or 4D dataset representing a feature of interest. To convert from the measurements to the real-valued feature an estimator must be applied. This thesis studies the development and evaluation of estimators. We approach the problem not as one of general image processing, but as one specific to MRI and based in the physics of the measurement process. The estimators proposed are based on the physics of MRI and protocols used clinically. We also show how estimators can be evaluated by testing suitability for radiological tasks. We present statistical models for protocols and features of interest that arise in MRI. Since the models contain nuisance parameters many estimators are available from the statistical theory. Additionally, we consider how adding a constraint of regularity in the phase coordinate of the complex data affects the estimators. We demonstrate how phase regularity can be integrated into the model using estimation with local models and avoiding a costly unwrapping step. To choose among the variety of estimators available for a model, we suggest task-based quality metrics. In particular, for estimators whose output is destined to be viewed by a radiologist, we demonstrate human observer studies and models of human perception that can quantify the quality of an estimator. For features of interest that are analyzed quantitatively, we study the trade-offs between bias and variance that are available. We find that choosing an estimator specific to the feature of interest and protocol can produce substantially improved output. Additionally, we find that our human observer results are not predicted by SNR, challenging the use of SNR for quantifying estimator suitability. We conclude that MRI-specific estimation and evaluation provide substantial advantages over general-purpose approaches.
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