Point Detection and Hotelling Discriminant: An Application in Adaptive Optics

Student: Luca Caucci

The detection of point objects has recently become an interesting topic in astronomy. Current applications include the detection of extrasolar planets as well as near-earth asteroids. Adaptive-optics systems have emerged as powerful instruments for astronomical observation; the basic structure of an adaptive-optics system is shown below:

Astronomical images obtained from adaptive optics systems can be thought of as realizations of spatiotemporal random processes; in these cases, the sources of randomness that influence astronomical imagery are the CCD noise in the science camera, the variability over time of the partially corrected point-spread function (PSF) and the unknown position and characteristics of the object(s) of interest. Current practice in astronomical point detection does not fully take advantage of the statistical properties of the temporal sequence of images obtained from adaptive-optics systems. For this reason, conventional state-of-the-art algorithms for point-object detection are suboptimal.

In a recent theoretical study carried out by Barrett et. al., the theory of object assessment of image quality has been extended and applied to adaptive-optics systems. Although this theory turns out to be too complicated to allow a complete analytical understanding, there are some alternatives.

In this research project, we used simulation to carry out a performance analysis of the spatiotemporal Hotelling discriminant for planet detection (see figure below). We demonstrated how the Hotelling discriminant can be applied in practical cases and which improvements over current techniques for planet detection can be achieved. This research posed several challenges; some of them are the generation of good estimations of first- and second-order statistics for the PSF contribution to the spatiotemporal covariance matrix, the ability to take advance of the particular structure of this matrix in order to store and manipulate it and, in particular, compute its inverse. Because of the optimality with respect to the area under the receiver-operator characteristic of the Hotelling discriminant among all the linear discriminants, this new technique outperformed previous algorithms for planet detection using the test images that we examined.

This work is a collaborative effort with Prof. Harrison H. Barrett, Dept. of Radiology, University of Arizona College of Medicine.