On the minimal number of measurements in low-rank matrix recovery

Kabanava, Maryia; Rauhut, Holger und Terstiege, Ulrich (2015): On the minimal number of measurements in low-rank matrix recovery. 2015 International Conference on Sampling Theory and Applications (SampTA), Washington, DC, 25-29 May 2015. In: 2015 International Conference on Sampling Theory and Applications (SampTA), IEEE. S. 382-386

Abstract

In this paper we present a new way to obtain a bound on the number of measurements sampled from certain distributions that guarantee uniform stable and robust recovery of low-rank matrices. The recovery guarantees are characterized by a stable and robust version of the null space property and verifying this condition can be reduced to the problem of obtaining a lower bound for a quantity of the form infxϵT||Ax||2. Gordon's escape through a mesh theorem provides such a bound with explicit constants for Gaussian measurements. Mendelson's small ball method allows to cover the significantly more general case of measurements generated by independent identically distributed random variables with finite fourth moment.

• Dokumententyp: Konferenzbeitrag (Paper)
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Lehrstuhl für Mathematik der Informationsverarbeitung
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch