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Optimal Spectral Reconstructions From Deterministic And Stochastic Sampling Geometries Using Compressive Sensing And Spectral Statistical Models, Oliver Jeromin

Electrical and Computer Engineering ETDs

This dissertation focuses on the development of high-quality image reconstruction methods from a limited number of Fourier samples using optimized, stochastic and deterministic sampling geometries. Two methodologies are developed: an optimal image reconstruction framework based on Compressive Sensing (CS) techniques and a new, Spectral Statistical approach based on the use of isotropic models over a dyadic partitioning of the spectrum. The proposed methods are demonstrated in applications in reconstructing fMRI and remote sensing imagery. Typically, a reduction in MRI image acquisition time is achieved by sampling K-space at a rate below the Nyquist rate. Various methods using correlation between samples, …