Inverse Problems with Sparsity Constraints is popular PDF and ePub book, written by Dennis Trede in 2010, it is a fantastic choice for those who relish reading online the Computers genre. Let's immerse ourselves in this engaging Computers book by exploring the summary and details provided below. Remember, Inverse Problems with Sparsity Constraints can be Read Online from any device for your convenience.
Inverse Problems with Sparsity Constraints Book PDF Summary
This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.
Detail Book of Inverse Problems with Sparsity Constraints PDF
- Author : Dennis Trede
- Release : 20 September 2024
- Publisher : Logos Verlag Berlin GmbH
- ISBN : 9783832524661
- Genre : Computers
- Total Page : 137 pages
- Language : English
- PDF File Size : 15,8 Mb
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