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Constrained regularization with the L1 norm for ill-posed problems

Shi, Mingren (1997) Constrained regularization with the L1 norm for ill-posed problems. PhD thesis, Murdoch University.

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Abstract

Many advances in modern science and technology have resulted in linear ill-posed problems, whose operator form is Kf = g, with possibly some constraints on the solution (e.g. non-negativity). The prototype example is a Fredholm integral equation of the first kind. An effective and prominent approach to cope with the instability of these problems is known as regularization. Most existing regularization methods are based on the L2 norm and this approach is now well-developed.

This thesis aims to develop a practical, general regularization method using the Li norm in both unconstrained and linearly constrained cases...

Item Type: Thesis (PhD)
Murdoch Affiliation: School of Physical Sciences, Engineering and Technology
Notes: Note to the author: If you would like to make your thesis openly available on Murdoch University Library's Research Repository, please contact: repository@murdoch.edu.au. Thank you.
Supervisor(s): Lukas, Mark and Hocking, Graeme
URI: http://researchrepository.murdoch.edu.au/id/eprint/51534
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