ASU Electronic Theses and Dissertations
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High-order methods are known for their accuracy and computational performance when applied to solving partial differential equations and have widespread use in representing images compactly. Nonetheless, high-order methods have difficulty representing functions containing discontinuities or functions having slow spectral decay in the chosen basis. Certain sensing techniques such as MRI and SAR provide data in terms of Fourier coefficients, and thus prescribe a natural high-order basis. The field of compressed sensing has introduced a set of techniques based on $\ell^1$ regularization that promote sparsity and facilitate working with functions having discontinuities. In this dissertation, high-order methods and $\ell^1$ regularization are …
- Denker, Dennis, Gelb, Anne, Archibald, Richard, et al.
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