Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements

Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta und Ma, Jackie (2015): Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. In: SIAM Journal on Mathematical Analysis, Bd. 47, Nr. 2: S. 1196-1233

Abstract

In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly supported wavelets and boundary wavelets. We prove that the number of samples that must be acquired to ensure a stable and accurate reconstruction scales linearly with the dimension of the wavelet reconstruction spaces. We also provide numerical experiments that corroborate our theoretical results.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0036-1410
• Sprache: Englisch