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title:
Quality assessment of the l1 penalization method for sparse recovery |
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name:
Verhoeven |
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first name:
Caroline
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location/conference:
cssip10
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PREPRINT-link:
http://arxiv.org/abs/0908.3636 |
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event/dateien/talks_cssip/verhoeven.pdf |
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abstract:
The l1 penalization method is often used for sparse recovery in (linear) inverse problems. Most research on the effectiveness of this method focuses on measurement matrices with mutual incoherent columns or which satisfy the restricted isometry property.
We will study matrices which do not satisfy these properties. Some typical recovery errors are computed in order to show how they are influenced by the sparsity of the desired solution, the noise level in the data, the number of data and the singular value spectrum of the matrix. These results are compared to known theoretical bounds. We also illustrate the ability of this method to predict relative errors on a magnetic tomography example. (joint work with I. Loris) |
