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This investigation seeks to establish the practicality of numerical frameapproximations. Specifically, it develops a new method to approximate theinverse frame operator and analyzes its convergence properties. It isestablished that sampling with {\em well-localized frames} improves both theaccuracy of the numerical frame approximation as well as the robustness andefficiency of the (finite) frame operator inversion. Moreover, in applicationssuch as magnetic resonance imaging, where the given data often may notconstitute a well-localized frame, a technique is devised to project thecorresponding frame data onto a more suitable frame. As a result, the targetfunction may be approximated as a finite expansion with its asymptoticconvergence solely dependent on its smoothness. Numerical examples areprovided.

Approximating the Inverse Frame Operator from Localized Frames