  A starshade suppresses starlight by a factor of 1E11 in the image plane of a
telescope, which is crucial for directly imaging Earth-like exoplanets. The
state of the art in high contrast post-processing and signal detection methods
were developed specifically for images taken with an internal coronagraph
system and focus on the removal of quasi-static speckles. These methods are
less useful for starshade images where such speckles are not present. This
paper is dedicated to investigating signal processing methods tailored to work
efficiently on starshade images. We describe a signal detection method, the
generalized likelihood ratio test (GLRT), for starshade missions and look into
three important problems. First, even with the light suppression provided by
the starshade, rocky exoplanets are still difficult to detect in reflected
light due to their absolute faintness. GLRT can successfully flag these dim
planets. Moreover, GLRT provides estimates of the planets' positions and
intensities and the theoretical false alarm rate of the detection. Second,
small starshade shape errors, such as a truncated petal tip, can cause
artifacts that are hard to distinguish from real planet signals; the detection
method can help distinguish planet signals from such artifacts. The third
direct imaging problem is that exozodiacal dust degrades detection performance.
We develop an iterative generalized likelihood ratio test to mitigate the
effect of dust on the image. In addition, we provide guidance on how to choose
the number of photon counting images to combine into one co-added image before
doing detection, which will help utilize the observation time efficiently. All
the methods are demonstrated on realistic simulated images.
