Sparse recovery on Euclidean Jordan algebras
This paper is concerned with the problem of sparse recovery on Euclidean Jordan algebra (SREJA), which includes the sparse signal recovery problem and the low-rank symmetric matrix recovery problem as special cases. We introduce the notions of restricted isometry property (RIP), null space property...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Elsevier BV
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/20281 |
| _version_ | 1848750262949249024 |
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| author | Kong, L. Sun, Jie Tao, J. Xiu, N. |
| author_facet | Kong, L. Sun, Jie Tao, J. Xiu, N. |
| author_sort | Kong, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper is concerned with the problem of sparse recovery on Euclidean Jordan algebra (SREJA), which includes the sparse signal recovery problem and the low-rank symmetric matrix recovery problem as special cases. We introduce the notions of restricted isometry property (RIP), null space property (NSP), and s-goodness for linear transformations in s-SREJA, all of which provide sufficient conditions for s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Moreover, we show that both the s-goodness and the NSP are necessary and sufficient conditions for exact s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Applying these characteristic properties, we establish the exact and stable recovery results for solving SREJA problems via nuclear norm minimization. |
| first_indexed | 2025-11-14T07:34:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-20281 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:34:03Z |
| publishDate | 2015 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-202812019-02-19T05:35:00Z Sparse recovery on Euclidean Jordan algebras Kong, L. Sun, Jie Tao, J. Xiu, N. Exact and stable recovery s-goodness Sparse recovery on Euclidean Jordan algebra Null space property Restricted isometry property Nuclear norm minimization This paper is concerned with the problem of sparse recovery on Euclidean Jordan algebra (SREJA), which includes the sparse signal recovery problem and the low-rank symmetric matrix recovery problem as special cases. We introduce the notions of restricted isometry property (RIP), null space property (NSP), and s-goodness for linear transformations in s-SREJA, all of which provide sufficient conditions for s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Moreover, we show that both the s-goodness and the NSP are necessary and sufficient conditions for exact s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Applying these characteristic properties, we establish the exact and stable recovery results for solving SREJA problems via nuclear norm minimization. 2015 Journal Article http://hdl.handle.net/20.500.11937/20281 10.1016/j.laa.2014.09.018 Elsevier BV fulltext |
| spellingShingle | Exact and stable recovery s-goodness Sparse recovery on Euclidean Jordan algebra Null space property Restricted isometry property Nuclear norm minimization Kong, L. Sun, Jie Tao, J. Xiu, N. Sparse recovery on Euclidean Jordan algebras |
| title | Sparse recovery on Euclidean Jordan algebras |
| title_full | Sparse recovery on Euclidean Jordan algebras |
| title_fullStr | Sparse recovery on Euclidean Jordan algebras |
| title_full_unstemmed | Sparse recovery on Euclidean Jordan algebras |
| title_short | Sparse recovery on Euclidean Jordan algebras |
| title_sort | sparse recovery on euclidean jordan algebras |
| topic | Exact and stable recovery s-goodness Sparse recovery on Euclidean Jordan algebra Null space property Restricted isometry property Nuclear norm minimization |
| url | http://hdl.handle.net/20.500.11937/20281 |