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

Mathematics of Super-Resolution Biomedical Imaging

by H. Ammari and J. Garnier and H. Kang and L. H. Nguyen and L. Seppecher

(Report number 2016-31)

Abstract
Super-resolution imaging is a collective name for a number of emerging techniques that achieve resolution below the conventional resolution limit, defined as the minimum distance that two point-source objects have to be in order to distinguish the two sources from each other. In these lecture notes we describe recent advances in scale separation techniques, spectroscopic approaches, multi-wave imaging, and nanoparticle imaging. The objective is fivefold: (i) To provide asymptotic expansions for both internal and boundary perturbations that are due to the presence of small anomalies; (ii) To apply those asymptotic formulas for the purpose of identifying the material parameters and certain geometric features of the anomalies; (iii) To design efficient inversion algorithms in multi-wave modalities; (iv) to develop inversion techniques using multi-frequency measurements; (v) to develop a mathematical and numerical framework for nanoparticle imaging. Applications of the anomaly detection and multi-wave approaches in medical imaging are described in some detail. In particular, the use of asymptotic analysis to improve a multitude of emerging imaging techniques is highlighted. These imaging modalities include both single-wave and multi-wave approaches. They can be divided into three groups: (i) Those using boundary or scattering measurements such as electrical impedance tomography, ultrasound, and infrared tomographies; (ii) Those using internal measurements such as magnetic resonance elastography; (iii) Those using boundary measurements obtained from internal perturbations of the medium such as photoacoustic tomography, impediography, and magnetoacoustic imaging.

Keywords: Hybrid imaging; Super-resolution; Mathematical Imaging.

@Techreport{AGKNS16_668,
  author = {H. Ammari and J. Garnier and H. Kang and L. H. Nguyen and L. Seppecher},
  title = {Mathematics of Super-Resolution Biomedical Imaging},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-31},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-31.pdf },
  year = {2016}
}

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).