Homomorphic sensing of subspace arrangements.
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| Title: | Homomorphic sensing of subspace arrangements. |
|---|---|
| Authors: | Peng, Liangzu1 (AUTHOR) penglz@shanghaitech.edu.cn, Tsakiris, Manolis C.1 (AUTHOR) mtsakiris@shanghaitech.edu.cn |
| Source: | Applied & Computational Harmonic Analysis. Nov2021, Vol. 55, p466-485. 20p. |
| Subjects: | Missing data (Statistics), Linear operators, Authorship, Compressed sensing, Map collections, Algebraic geometry |
| Abstract: | Homomorphic sensing is a recent algebraic-geometric framework that studies the unique recovery of points in a linear subspace from their images under a given collection of linear maps. It has been successful in interpreting such a recovery in the case of permutations composed by coordinate projections, an important instance in applications known as unlabeled sensing, which models data that are out of order and have missing values. We provide tighter and simpler conditions guaranteeing the unique recovery for the single-subspace case, and we extend the result to subspace arrangements and noisy measurements. We specialize our results to homomorphic sensing examples such as real phase retrieval and unlabeled sensing. In so doing, in a unified way, we obtain conditions guaranteeing the unique recovery for those examples, typically known via diverse techniques in the literature, as well as novel conditions for sparse and unsigned versions of unlabeled sensing. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied & Computational Harmonic Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 151856804 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Homomorphic sensing of subspace arrangements. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Peng%2C+Liangzu%22">Peng, Liangzu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> penglz@shanghaitech.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Tsakiris%2C+Manolis+C%2E%22">Tsakiris, Manolis C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mtsakiris@shanghaitech.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+%26+Computational+Harmonic+Analysis%22">Applied & Computational Harmonic Analysis</searchLink>. Nov2021, Vol. 55, p466-485. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Missing+data+%28Statistics%29%22">Missing data (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+operators%22">Linear operators</searchLink><br /><searchLink fieldCode="DE" term="%22Authorship%22">Authorship</searchLink><br /><searchLink fieldCode="DE" term="%22Compressed+sensing%22">Compressed sensing</searchLink><br /><searchLink fieldCode="DE" term="%22Map+collections%22">Map collections</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+geometry%22">Algebraic geometry</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Homomorphic sensing is a recent algebraic-geometric framework that studies the unique recovery of points in a linear subspace from their images under a given collection of linear maps. It has been successful in interpreting such a recovery in the case of permutations composed by coordinate projections, an important instance in applications known as unlabeled sensing, which models data that are out of order and have missing values. We provide tighter and simpler conditions guaranteeing the unique recovery for the single-subspace case, and we extend the result to subspace arrangements and noisy measurements. We specialize our results to homomorphic sensing examples such as real phase retrieval and unlabeled sensing. In so doing, in a unified way, we obtain conditions guaranteeing the unique recovery for those examples, typically known via diverse techniques in the literature, as well as novel conditions for sparse and unsigned versions of unlabeled sensing. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied & Computational Harmonic Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.acha.2021.06.008 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 466 Subjects: – SubjectFull: Missing data (Statistics) Type: general – SubjectFull: Linear operators Type: general – SubjectFull: Authorship Type: general – SubjectFull: Compressed sensing Type: general – SubjectFull: Map collections Type: general – SubjectFull: Algebraic geometry Type: general Titles: – TitleFull: Homomorphic sensing of subspace arrangements. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Peng, Liangzu – PersonEntity: Name: NameFull: Tsakiris, Manolis C. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 10635203 Numbering: – Type: volume Value: 55 Titles: – TitleFull: Applied & Computational Harmonic Analysis Type: main |
| ResultId | 1 |
