The convex algebraic geometry of linear inverse problems
We study a class of ill-posed linear inverse problems in which the underlying model of interest has simple algebraic structure. We consider the setting in which we have access to a limited number of linear measurements of the underlying model, and we propose a general framework based on convex optim...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/72963 https://orcid.org/0000-0003-1132-8477 https://orcid.org/0000-0003-0149-5888 |
| _version_ | 1826199517555326976 |
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| author | Chandrasekaran, Venkat Recht, Benjamin Parrilo, Pablo A. Willsky, Alan S. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Chandrasekaran, Venkat Recht, Benjamin Parrilo, Pablo A. Willsky, Alan S. |
| author_sort | Chandrasekaran, Venkat |
| collection | MIT |
| description | We study a class of ill-posed linear inverse problems in which the underlying model of interest has simple algebraic structure. We consider the setting in which we have access to a limited number of linear measurements of the underlying model, and we propose a general framework based on convex optimization in order to recover this model. This formulation generalizes previous methods based on ℓ[subscript 1]-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices from a small number of linear measurements. For example some problems to which our framework is applicable include (1) recovering an orthogonal matrix from limited linear measurements, (2) recovering a measure given random linear combinations of its moments, and (3) recovering a low-rank tensor from limited linear observations. |
| first_indexed | 2024-09-23T11:21:13Z |
| format | Article |
| id | mit-1721.1/72963 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:21:13Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/729632022-10-01T03:01:47Z The convex algebraic geometry of linear inverse problems Chandrasekaran, Venkat Recht, Benjamin Parrilo, Pablo A. Willsky, Alan S. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Parrilo, Pablo A. Chandrasekaran, Venkat Parrilo, Pablo A. Willsky, Alan S. We study a class of ill-posed linear inverse problems in which the underlying model of interest has simple algebraic structure. We consider the setting in which we have access to a limited number of linear measurements of the underlying model, and we propose a general framework based on convex optimization in order to recover this model. This formulation generalizes previous methods based on ℓ[subscript 1]-norm minimization and nuclear norm minimization for recovering sparse vectors and low-rank matrices from a small number of linear measurements. For example some problems to which our framework is applicable include (1) recovering an orthogonal matrix from limited linear measurements, (2) recovering a measure given random linear combinations of its moments, and (3) recovering a low-rank tensor from limited linear observations. 2012-09-14T15:56:55Z 2012-09-14T15:56:55Z 2010-09 2010-09 Article http://purl.org/eprint/type/ConferencePaper 978-1-4244-8215-3 http://hdl.handle.net/1721.1/72963 Chandrasekaran, Venkat et al. “The Convex Algebraic Geometry of Linear Inverse Problems.” 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2010. 699–703. © Copyright 2010 IEEE https://orcid.org/0000-0003-1132-8477 https://orcid.org/0000-0003-0149-5888 en_US http://dx.doi.org/10.1109/ALLERTON.2010.5706975 Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2010 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers (IEEE) IEEE |
| spellingShingle | Chandrasekaran, Venkat Recht, Benjamin Parrilo, Pablo A. Willsky, Alan S. The convex algebraic geometry of linear inverse problems |
| title | The convex algebraic geometry of linear inverse problems |
| title_full | The convex algebraic geometry of linear inverse problems |
| title_fullStr | The convex algebraic geometry of linear inverse problems |
| title_full_unstemmed | The convex algebraic geometry of linear inverse problems |
| title_short | The convex algebraic geometry of linear inverse problems |
| title_sort | convex algebraic geometry of linear inverse problems |
| url | http://hdl.handle.net/1721.1/72963 https://orcid.org/0000-0003-1132-8477 https://orcid.org/0000-0003-0149-5888 |
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