ASU Electronic Theses and Dissertations
- 2 English
- 2 Public
Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. …
- Scarnati, Theresa Ann, Gelb, Anne, Platte, Rodrigo, et al.
- Created Date
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.
- Created Date