Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure

Accelerated Imaging Techniques for Chemical Shift Magnetic Resonance Imaging

Chemical shift imaging is a method for the separation two or more chemical species. The cost of chemical shift encoding is increased acquisition time as multiple acquisitions are acquired at different echo times. Image acceleration techniques, typically parallel imaging, are often used to improve the spatial coverage and resolution. This thesis describes a new technique for estimating the signal to noise ratio for parallel imaging reconstructions and proposes new image reconstructions for accelerated chemical shift imaging using compressed sensing and/or parallel imaging for two applications: water-fat separation and metabolic imaging of hyperpolarized [1-13C] pyruvate. Spatially varying noise in parallel imaging reconstructions makes measurements of the signal to noise ratio, a commonly used metric for image for image quality, difficult. Existing approaches have limitations such as they are not applicable to all reconstructions, require significant computation time, or rely on repeated image acquisitions. A SNR estimation technique is proposed that does not exhibit these limitations. Water-fat imaging of highly undersampled datasets from the liver, calf, knee, and abdominal cavity are demonstrated using a customized IDEAL-SPGR pulse sequence and an integrated compressed sensing, parallel imaging, water-fat reconstruction. This method is shown to offer comparable image quality relative to fully sampled reference images for a range of acceleration factors. At high acceleration factors, this technique is shown to offer improved image quality when compared to the current standard of parallel imaging. Accelerated chemical shift imaging was demonstrated for metabolic of hyperpolarized [1-13C] pyruvate. Pyruvate, lactate, alanine, and bicarbonate images were reconstructed from undersampled datasets. Phantoms were used to validate this technique while retrospectively and prospectively accelerated 3D in vivo datasets were used to demonstrate. Alternatively, acceleration was also achieved through the use of a high performance magnetic field gradient set. This thesis addresses the inherently slow acquisition times of chemical shift imaging by examining the role compressed sensing and parallel imaging can be play in chemical shift imaging. An approach to SNR assessment for parallel imaging reconstruction is proposed and approaches to accelerated chemical shift imaging are described for applications in water-fat imaging and metabolic imaging of hyperpolarized [1-13C] pyruvate

Development of Advanced Acquisition and Reconstruction Techniques for Real-Time Perfusion MRI

Diese Doktorarbeit befasst sich mit der methodischen Entwicklung von Akquisition- und Rekonstruktionstechniken zur Anwendung von Echtzeit-Bildgebungstechniken auf das Gebiet der dynamischen kontrastmittelgestützten Magentresonanztomographie. Zur Unterdrückung unerwünschter Bildartefakte wird eine neue Spoiling-Technik vorgeschlagen, die auf randomisierten Phasen der Hochfrequenzanregung basiert. Diese Technik erlaubt eine schnelle, artefaktfreie Aufnahme von T1-gewichteten Rohdaten bei radialer Abtastung. Die Rekonstruktion quantitativer Parameterkarten aus solchen Rohdaten kann als nichtlineares, inverses Problem aufgefasst werden. In dieser Arbeit wird eine modellbasierte Rekonstruktionstechnik zur quantitativen T1-Kartierung entwickelt, die dieses inverse Problem mittels der iterativ regularisierten Gauß-Newton-Methode mit parameterspezifischer Regularisierung löst. In Simulationen sowie in-vitro- und in-vivo-Studien wird Genauigkeit und Präzision dieser neuen Methode geprüft, die ihre direkte Anwendung in in-vitro-Experimenten zur "first-pass"-Perfusion findet. In diesen Experimenten wird ein kommerziell verfügbares Phantom verwendet, dass in-vivo-Perfusion simuliert und gleichzeitig vollständige Kontrolle über die vorherrschenden Austauschraten erlaubt

Robust inversion and detection techniques for improved imaging performance

Thesis (Ph.D.)--Boston UniversityIn this thesis we aim to improve the performance of information extraction from imaging systems through three thrusts. First, we develop improved image formation methods for physics-based, complex-valued sensing problems. We propose a regularized inversion method that incorporates prior information about the underlying field into the inversion framework for ultrasound imaging. We use experimental ultrasound data to compute inversion results with the proposed formulation and compare it with conventional inversion techniques to show the robustness of the proposed technique to loss of data. Second, we propose methods that combine inversion and detection in a unified framework to improve imaging performance. This framework is applicable for cases where the underlying field is label-based such that each pixel of the underlying field can only assume values from a discrete, limited set. We consider this unified framework in the context of combinatorial optimization and propose graph-cut based methods that would result in label-based images, thereby eliminating the need for a separate detection step. Finally, we propose a robust method of object detection from microscopic nanoparticle images. In particular, we focus on a portable, low cost interferometric imaging platform and propose robust detection algorithms using tools from computer vision. We model the electromagnetic image formation process and use this model to create an enhanced detection technique. The effectiveness of the proposed technique is demonstrated using manually labeled ground-truth data. In addition, we extend these tools to develop a detection based autofocusing algorithm tailored for the high numerical aperture interferometric microscope