This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that sampling with well-localized frames improves both the accuracy of the numerical frame approximation as well as the robustness and efficiency of the (finite) frame operator inversion. Moreover, in applications such as magnetic resonance imaging, where the given data often may not constitute a well-localized frame, a technique is devised to project the corresponding frame data onto a more suitable frame. As a result, the target function may be approximated as a finite expansion with its asymptotic convergence solely dependent on its smoothness. Numerical examples are provided.
Details
- Approximating the Inverse Frame Operator From Localized Frames
- Song, Guohui (Author)
- Gelb, Anne (Author)
- College of Liberal Arts and Sciences (Contributor)
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Digital object identifier: 10.1016/j.acha.2012.08.002
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Identifier TypeInternational standard serial numberIdentifier Value1063-5203
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“NOTICE: this is the author’s version of a work that was accepted for publication in Applied and Computational Harmonic Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied and Computational Harmonic Analysis, 35(1), 94-110. doi:10.1016/j.acha.2012.08.002
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Song, G., & Gelb, A. (2013). Approximating the inverse frame operator from localized frames. Applied and Computational Harmonic Analysis, 35(1), 94-110. doi:10.1016/j.acha.2012.08.002