Research reports

Years: 2026 2025 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

On sharp stable recovery from clipped and folded measurements

by P. Abdalla and D. Freeman and J. Ramos and M. Taylor

(Report number 2025-19)

Abstract
We investigate the stability of vector recovery from random linear measurements which have been either clipped or folded. This is motivated by applications where measurement devices detect inputs outside of their effective range. As examples of our main results, we prove sharp lower bounds on the recovery constant for both the declipping and unfolding problems whenever samples are taken according to a uniform distribution on the sphere. Moreover, we identify (almost) optimal conditions on both the number of samples and the distribution of the data for these estimates to hold, and we prove that such estimates are the best that any frame of normalized vectors can achieve. We then show that all of the above results have suitable (effectively) sparse counterparts. In the special case that one restricts the stability analysis to vectors which belong to the unit sphere of \(\mathbb{R}^n\), we show that the problem of declipping directly extends the one-bit compressed sensing results of Oymak-Recht and Plan-Vershynin.

Keywords: Saturation recovery, Unlimited sampling

@Techreport{AFRT25_1140,
  author = {P. Abdalla and D. Freeman and J. Ramos and M. Taylor},
  title = {On sharp stable recovery from clipped and folded measurements},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-19},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-19.pdf },
  year = {2025}
}

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).