A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging

A frame theoretic technique is introduced that combines Fourier and finite frames. The technique is based on fundamental theorems by Beurling and Landau in the theory of Fourier frames, and transitions to the finite frame case, where an algorithm is constructed. The algorithm exhibits the strengths of frame theory dealing with noise reduction and stable signal reconstruction. It was designed to resolve problems dealing with fast spectral data acquisition in magnetic resonance imaging (MRI), and has applicability to a larger class of signal reconstruction problems.