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Displacement of artefacts in inverse scattering

We analyse further inverse problems related to synthetic aperture radar imaging considered by Nolan and Cheney (2002 Inverse Problems 18 221). Under a nonzero curvature assumption, it is proved that the forward operator F is associated with a two-sided fold, C. To reconstruct the singularities in the wave speed, we form the normal operator F*F. In Felea (2005 Comm. Partial Diff. Eqns 30 1717) and Nolan (2000 SIAM J. Appl. Math. 61 659), it was shown that F*F ∊ I2m,0(Δ, C1), where C1 is another two-sided fold. In this case, the artefact on C1 has the same strength as the initial singularities on Δ and cannot be removed. By working away from the fold points, we construct recursively operators Qi which, when applied to F*F, migrate the primary artefact. One part is lower order, has less strength and is smoother than the image to be reconstructed. The other part is as strong as the original artefact, but is spatially separated from the scene.