Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Intrinsic localization of anisotropic frames

by P. Grohs

(Report number 2012-04)

Abstract
The present article studies o-diagonal decay properties of Moore-Penrose pseudoinverses of (bi-infinite) matrices satisfying an analogous condition. O-diagonal decay in our paper is considered with respect to specic index distance functions which incorporates those usually used for the study of localization properties for wavelet frames but also more general systems such as curvelets or shearlets. Our main result is that if a matrix satises an o-diagonal decay condition, then its Moore-Penrose pseudoinverse satisfies a similar condition. Applied to the study of frames this means that, if a wavelet, curvelet or shearlet frame is intrinsically localized, then its canonical dual is, too.

Keywords: Frame Localization, Curvelets, Shearlets, nonlinear Approximation

@Techreport{G12_446,
  author = {P. Grohs},
  title = {Intrinsic localization of anisotropic frames},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-04.pdf },
  year = {2012}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).