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Compressive Sensing With Prior Information Applied To Magnetic Resonance Imaging, Cristiano Jacques Miosso

Open Access Theses & Dissertations

This dissertation introduces the theory of compressive sensing with prior information about a signal's sparse representation. We show, mathematically and in numerical simulations, that prior information improves signal reconstruction, in terms of number of required measurements, computation time and signal-to-noise ratios. Following, we present a set of methods for enhanced magnetic resonance imaging and tomography that can be combined with prior information, for enhanced image quality.

In developing the theory of compressive sensing with prior information, we provide a mathematical proof of the required condition (in terms of number of linear measurements) for reconstruction using the ideal approach of l0-minimization, …