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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Inverse Problems with Sparsity Constraints: Convergence Rates and Exact Recovery

Inverse Problems with Sparsity Constraints: Convergence Rates and Exact Recovery

Trede, Dennis

Paperback

General ComputersGeneral MathematicsPhysics

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ISBN10: 3832524665
ISBN13: 9783832524661
Publisher: Logos Verlag Berlin
Published: May 20 2010
Pages: 137
Weight: 0.40
Height: 0.33 Width: 5.76 Depth: 8.20
Language: English
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.

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