On Invertibility of the Radon Transform and Compressive Sensing
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , vii, 30 p.
Radon transform, invertibility, compressive sensing, stability estimates
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-141837ISBN: 978-91-7501-998-7OAI: oai:DiVA.org:kth-141837DiVA: diva2:698802
2014-03-28, D3, Lindstedtsvägen 5, Stockholm, 13:00 (English)
Salo, Mikko, Professor
Strömberg, Jan-Olov, Professor
FunderKnut and Alice Wallenberg Foundation, KAW 2005.0098
QC 201402282014-02-282014-02-252014-02-28Bibliographically approved
List of papers