Image reconstruction from Fourier samples

Researchers: Ben Adcock (Simon Fraser University), Milana Gataric, Anders Hansen

We developed a robust reconstruction framework, known as generalized sampling, which allows an image to be approximated in sparse or rapidly-convergent representation systems using only its Fourier samples obtained not necessarily on a Cartesian grid. Non-Cartesian sampling is of a particular importance in MRI, as non-uniform patterns facilitate faster imaging. We investigated the rate of convergence of such approximate solutions and their numerical stability and derived the results that allow us to relate sufficient and necessary conditions for robust recovery under different sampling scenarios.

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