Exterior/interior problem for the circular means transform with applications to intravascular imaging
Abstract
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 tomographylike reconstruction in these modalities.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 DOI:
 10.48550/arXiv.1308.6016
 arXiv:
 arXiv:1308.6016
 Bibcode:
 2013arXiv1308.6016A
 Keywords:

 Mathematics  Analysis of PDEs;
 44A12;
 65M32;
 92C55