Scattering in the Presence of Fold Caustics

<title>Microlocal high-range-resolution ISAR for low signal-to-noise environments</title>

“…In particular, analysis of wavefront sets can determine whether backprojection will provide an image free of certain artifacts. 16,21,34 In addition, wavefront-set analysis suggests an approach for producing artifact-free, superresolved images: remove all components of the data set except those that correspond to well-understood target features, and form an image from those components only.…”

An FIO Calculus for Marine Seismic Imaging: Folds and Cross Caps

“…We then establish a composition calculus for general FIOs associated with similar canonical relations, which we call folded cross caps, sufficient for identifying the normal operator F * F . In contrast to the case of a single source experiment, treated by Nolan [25] and Felea[5], the resulting artifact is 1 2 order smoother than the main pseudodifferential part of F * F . …”

“…The assumption (ii) ensures that F is an FIO ( [15], [18], [29], [28]) and (i) ensures that the composition F * F makes sense. In the case of the single source model, with only fold caustics appearing, Nolan [25] showed that F is an FIO associated to a folding canonical relation in the sense of [21] (also called a two-sided fold), and stated that the Schwartz kernel of the operator F * F belongs to a class of distributions associated to two cleanly intersecting Lagrangians in (T * Y \ 0) × (T * Y \ 0). This was fully proved in [5].…”

“…Composition of FIOs under other singular geometries arising in integral geometry and inverse problems has been previously studied in, e.g., [13], [9], [11], [12], [25] and [5].…”

“…We find a weak normal form for any folded cross cap canonical relation C ⊂ T * X × T * Y which allows us to show that F * F ∈ I p,l (∆,C), withC a folding canonical relation in T * Y × T * Y . We would like to thank Cliff Nolan for the helpful discussions, clarifying [25], at the Institute for Mathematics and its Applications, Minneapolis, in October, 2005.…”