Microlocal analysis of a spindle transform

Abstract

An analysis of the stability of the spindle transform, introduced in [16], is presented. We do this via a microlocal approach and show that the normal operator for the spindle transform is a type of paired Lagrangian operator with “blowdown-blowdown” singularities analogous to that of a limited data synthetic aperture radar (SAR) problem studied by Felea et. al. [4]. We find that the normal operator for the spindle transform belongs to a class of distibutions Ip,l(Δ,Λ)+Ip,l(Δ,Λ) studied by Felea and Marhuenda in [4,10], where Δ is reflection through the origin, and Λ is associated to a rotation artefact. Later, we derive a filter to reduce the strength of the image artefact and show that it is of convolution type. We also provide simulated reconstructions to show the artefacts produced by Λ and show how the filter we derived can be applied to reduce the strength of the artefact.