Application of the Hotelling and ideal observers to detection and localization of exoplanets

Abstract

The ideal linear discriminant or Hotelling observer is widely used for detection tasks and imagequality assessment in medical imaging, but it has had little application in other imaging fields. We apply it to detection of planets outside of our solar system with long-exposure images obtained from ground-based or space-based telescopes. The statistical limitations in this problem include Poisson noise arising mainly from the host star, electronic noise in the image detector, randomness or uncertainty in the point-spread function (PSF) of the telescope, and possibly a random background. PSF randomness is reduced but not eliminated by the use of adaptive optics. We concentrate here on the effects of Poisson and electronic noise, but we also show how to extend the calculation to include a random PSF. For the case where the PSF is known exactly, we compare the Hotelling observer to other observers commonly used for planet detection; comparison is based on receiver operating characteristic (ROC) and localization ROC (LROC) curves.

Spatio-temporal Hotelling observer for signal detection from image sequences

“…The results of Fig. 1 complete the ones reported in [25]. Indeed, in [25], we compared the spatial Hotelling observer with current techniques used in astronomy for point-source detection, and we noted that the spatial Hotelling observer outperforms popular detection algorithms, such as [46].…”

“…Differences between the actual mean and covariance present in real data and the mean and covariance used in the detection task can arise from two sources: errors in the simulation code or sampling errors because the mean and covariance are estimated from a finite number of simulated sample images. In this work and related previous studies [25,47], we have investigated the latter point in great detail. The former point, effect of model errors on detection performance, has not been investigated for the spatiotemporal Hotelling observer (implemented for the first time in this paper), but it has been studied in the medical literature for purely spatial Hotelling observers [21,48].…”

“…The more realistic problem of unknown signal location can be handled by scanning the observer template [24–26]. The SKE hypothesis provides valuable information that the observer can use to improve detection performance (quantified by an increase in AUC) with respect to the detection and localization problem of [25]. We also assume that the object background is known exactly (background-known-exactly or BKE in the terminology of [21]).…”

On advanced estimation techniques for exoplanet detection and characterization using ground-based coronagraphs

“…2, 3 Moreover, it has been shown that the so-called spatio-temporal Hotelling observer significantly outperforms not only the current long-exposure detection algorithms, but it is also a much better approach, in terms of AUC, than the purely spatial Hotelling observer. 5 On the other hand, the assumptions that went into these simulated tests, such as the availability of noise-free training data might be optimistic.…”

“…Four algorithms would be used: spatial Hotelling observer on long exposures, 3 spatio-temporal Hotelling observer on the sequences of short exposures, 5 statistical speckle discrimination on sequences of frames, 26 a combination of statistical speckle discrimination (as a pre-processing, object-amplifying step), and a subsequent application of the spatial Hotelling observer. The ROC curves would be constructed for each of these methods.…”