Exterior/interior problem for the circular means transform with applications to intravascular imaging

Gaik Ambartsoumian, Leonid Kunyansky

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Exterior inverse problem for the circular means transform (CMT) arises in the intravascular photoacoustic imaging (IVPA), in the intravascular ultrasound imaging (IVUS), as well as in radar and sonar. The reduction of the IPVA to the CMT is quite straightforward. As shown in the paper, in IVUS the circular means can be recovered from measurements by solving a certain Volterra integral equation. Thus, a tomography reconstruction in both modalities requires solving the exterior problem for the CMT. Numerical solution of this problem usually is not attempted due to the presence of "invisible" wavefronts, which results in severe instability of the reconstruction. The novel inversion algorithm proposed in this paper yields a stable partial reconstruction: it reproduces the "visible" part of the image and blurs the "invisible" part. If the image contains little or no invisible wavefronts (as frequently happens in the IVPA and IVUS) the reconstruction is quantitatively accurate. The presented numerical simulations demonstrate the feasibility of tomography-like reconstruction in these modalities.

Original languageEnglish (US)
Pages (from-to)339-359
Number of pages21
JournalInverse Problems and Imaging
Issue number2
StatePublished - May 2014


  • Circular means
  • Exterior problem
  • Intravas-cular imaging
  • Photoacoustic tomography
  • Radon transform

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization


Dive into the research topics of 'Exterior/interior problem for the circular means transform with applications to intravascular imaging'. Together they form a unique fingerprint.

Cite this