In synthetic aperture radar (SAR) imaging, a scene of interest is illuminated by electromagnetic waves. The aim
is to reconstruct an image of the scene from the measurement of the scattered waves using airborne antenna(s).
There are many imaging systems which are built upon this notion such as mono-static SAR, bi-static SAR, and
hitchhiker SAR. For these modalities, there are analytic reconstruction algorithms based on backprojection.
Backprojection-based algorithms have the advantage of putting the visible edges of the scene at the right location
and orientation in the reconstructed images.
On the other hand, there is also a SAR imaging method based on the generalized likelihood-ratio test (GLRT).
In particular we consider the problem of detecting a target at an unknown location. In the GLRT, the presence
of a target in the scene is determined based on the likelihood-ratio test. Since the location of the target is not
known, the GLRT test statistic is calculated for each position in the scene and the location corresponding to the
maximum test statistic indicates the location of a potential target.
In this paper, we show that the backprojection-based analytic reconstruction methods include as a special
case the GLRT method. We show that the GLRT test statistic is related to the reflectivity of the scene when a
backprojection-based reconstruction algorithm is used.