Electron paramagnetic resonance image reconstruction for arbitrary projection sampling and regions of interest

Electron Paramagnetic Resonance is a spectroscopic technique for the investigation of paramagnetic compounds such as free radicals. The extension of EPR to imaging (EPRI) provides for a powerful biomedical imaging modality capable of imaging radicals in vivo for a variety of small animals. Through spectroscopic imaging techniques, injected, stable, free radicals can be used to query their local microenvironment. Of particular interest is EPRI's ability to image oxygen concentrations in a non-invasive quantitative manner. Oxygen's powerful role in cancer pathology and treatment is driving the development of EPRI in terms of size, resolution, and acquisition speed.;Image reconstruction in EPRI is based on its modeling as a Radon transform and inversion by the Filtered Backprojection (FBP) algorithm. Current implementation of the FBP algorithm limits the performance of EPRI imaging when pursuing the various goals of accuracy, field of view and spatial resolution, ideally all with minimal acquisition time. The work of this dissertation has been the development of reconstruction methods specific to EPRI and the implications they may have for efficient sampling and acquisition. Single stage projections methods are developed as an accurate and flexible discretization of the Radon transform and its inversion. A sampling density compensation factor was derived from Voronoi decomposition of the surface of surface of the sphere for each projection direction. These were incorporated into simulation and reconstruction algorithms to facilitate a direct method of transforming between the image and projections spaces without data gridding requirements. With these new algorithms standard methods of projection smoothing and interpolation are reexamined. The performance of various frequency domain bandlimited filters was compared to a proposed non-linear method of Wavelet denoising in simulations of various SNR levels. Projection interpolation also had to be adapted to the single stage methods to handle interpolation of points in multiple dimensions without gridding. Finally a Backprojection Filtration (BPF) algorithm was proposed for reconstruction of four dimensional images from truncated projection data.