Array imaging of sparse scatterers
Abstract/Contents
- Abstract
- We consider narrow band (single frequency) array imaging of localized scatterers. We introduce a hybrid approach for coherent imaging using both the singular value decomposition (SVD) and L1 minimization so as to fully exploit the intrinsic sparsity contained in the array data. We compare the results with other imaging methods such as multiple signal classification, least squares and migration. We show that well-separated point scatterers can be recovered exactly with the hybrid L1 minimization. Moreover, using the SVD we determine the optimally subsampled array data for the L1 minimization. Numerical simulations confirm that this imaging approach is robust with respect to additive noise. Furthermore, with a simple random phase model for a heterogeneous medium, we also show that the hybrid L1 method is efficient for imaging with correlated noise arising from the random medium. For imaging without knowing the phase of data explicitly, we introduce a new approach for narrow band array imaging of localized scatterers from intensity-only measurements by considering the possibility of reconstructing the positions and reflectivities of the scatterers exactly from only partial knowledge of the array data. We reformulate this intensity-only imaging problem as a non-convex optimization problem and show that we can have exact recovery by minimizing the rank of a positive semidefinite matrix associated with the unknown reflectivities. Since this optimization problem is NP-hard and is computationally intractable, we replace the rank of the matrix by its nuclear norm, the sum of its singular values, which is a convex programming problem that can be solved in polynomial time. Numerical experiments explore the robustness of this approach, which recovers sparse reflectivity vectors exactly as solutions of a convex optimization problem.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Copyright date | 2011 |
| Publication date | 2010, c2011; 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Chai, Anwei |
|---|---|
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
| Primary advisor | Papanicolaou, George |
| Thesis advisor | Papanicolaou, George |
| Thesis advisor | Garapon, Pierre |
| Thesis advisor | Ryzhik, Leonid |
| Advisor | Garapon, Pierre |
| Advisor | Ryzhik, Leonid |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Anwei Chai. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2011. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Anwei Chai
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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