MICROLOCAL ANALYSIS OF SAR IMAGING OF A DYNAMIC REFLECTIVITY FUNCTION

In this article we consider four particular cases of synthetic aperture radar imaging with moving objects. In each case, we analyze the forward operator $F$ and the normal operator $F^*F$, which appear in the mathematical expression for the recovered reflectivity function (i.e., the image). In general, by applying the backprojection operator $F^*$ to the scattered waveform (i.e., the data), artifacts appear in the reconstructed image. In the first case, the full data case, we show that $F^*F$ is a pseudodifferential operator which implies that there is no artifact. In the other three cases, which have less data, we show that $F^*F$ belongs to a class of distributions associated to two cleanly intersecting Lagrangians $I^{p,l}(\Delta, \Lambda)$, where $\Lambda$ is associated to a strong artifact. At the and of the article, we show how to microlocally reduce the strength of the artifact.