DETECTION AND CHARACTERIZATION OF EXOPLANETS USING PROJECTIONS ON KARHUNEN–LOEVE EIGENIMAGES: FORWARD MODELING
A new class of high-contrast image analysis algorithms that empirically fit and subtract systematic noise has lead to recent discoveries of faint exoplanet/substellar companions and scattered light images of circumstellar disks. These methods are extremely efficient at enhancing the detectability of a faint astrophysical signal, but they generally create systematic biases in their observed properties. This paper provides a general solution for this outstanding problem. We present an analytical derivation of a linear expansion that captures the impact of astrophysical over-subtraction or self-subtraction in current image analysis techniques. We examine the general case for which the reference images of the astrophysical scene move azimuthally and/or radially across the field of view as a result of the observation strategy. Our new method is based on perturbing the covariance matrix underlying any least-squares speckles problem, and propagating this perturbation through the data analysis algorithm. Most of the work in this paper is presented in the Principal Component Analysis framework, but it can be easily generalized to methods relying on the linear combination of images (instead of eigenmodes). Based on this linear expansion, which is obtained in the most general case, we then demonstrate practical applications of this new algorithm. We first consider the spectral extraction of faint point sources in IFS data and illustrate, using public Gemini Planet Imager commissioning data, that our novel perturbation-based Forward Modeling, which we named Karhunen Loeve Image Processing (KLIP-FM), can indeed alleviate algorithmic biases. We then apply KLIP-FM to the detection of point sources and show how it decreases the rate of false negatives while keeping the rate of false positives unchanged when compared to classical KLIP. This can potentially have important consequences on the design of follow-up strategies of ongoing direct imaging surveys.