التفاصيل البيبلوغرافية
| العنوان: |
Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs |
| المؤلفون: |
Brugiapaglia, Simone, Dirksen, Sjoerd, Jung, Hans Christian, Rauhut, Holger, Sub Mathematical Modeling, Mathematical Modeling |
| المساهمون: |
Sub Mathematical Modeling, Mathematical Modeling |
| المصدر: |
Applied and Computational Harmonic Analysis, 53, 231. Academic Press Inc. |
| بيانات النشر: |
arXiv, 2020. |
| سنة النشر: |
2020 |
| مصطلحات موضوعية: |
Independent and identically distributed random variables, FOS: Computer and information sciences, Computer Science - Information Theory, Generic chaining, 010103 numerical & computational mathematics, Isometry (Riemannian geometry), 01 natural sciences, Upper and lower bounds, Restricted isometry constants, CORSING method, Taverne, FOS: Mathematics, Uniform boundedness, Applied mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Mathematics, Applied Mathematics, Information Theory (cs.IT), 010102 general mathematics, Numerical Analysis (math.NA), Covariance, Bounded Riesz systems, Compressive sensing, Bounded function, Bernoulli process, Numerical PDEs, Random matrix |
| الوصف: |
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of bounded Riesz systems and generalizes random partial Fourier matrices. Our main result improves the currently available results for the null space and restricted isometry properties of such random matrices. The main novelty of our analysis is a new upper bound for the expectation of the supremum of a Bernoulli process associated with a restricted isometry constant. We apply our result to prove new performance guarantees for the CORSING method, a recently introduced numerical approximation technique for partial differential equations (PDEs) based on compressive sensing. |
| وصف الملف: |
application/pdf |
| تدمد: |
1063-5203 |
| DOI: |
10.48550/arxiv.2005.06994 |
| URL الوصول: |
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e45b031ef09e3f76c3a683f1d4d795e3 |
| Rights: |
OPEN |
| رقم الانضمام: |
edsair.doi.dedup.....e45b031ef09e3f76c3a683f1d4d795e3 |
| قاعدة البيانات: |
OpenAIRE |