Likelihood ratio map for direct exoplanet detection Hazan Daglayan ICTEAM Institute

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Likelihood ratio map for direct exoplanet detection

Hazan Daglayan

ICTEAM Institute

UCLouvain

Louvain-la-Neuve, Belgium

hazan.daglayan@uclouvain.be

Simon Vary

ICTEAM Institute

UCLouvain

Louvain-la-Neuve, Belgium

simon.vary@uclouvain.be

Faustine Cantalloube

CNRS, CNES, LAM

Aix Marseille Univ

Marseille, France

faustine.cantalloube@lam.fr

P.-A. Absil

ICTEAM Institute

UCLouvain

Louvain-la-Neuve, Belgium

pa.absil@uclouvain.be

Olivier Absil

STAR Institute

Universit´

e de Li`

ege

Li`

ege, Belgium

olivier.absil@uliege.be

Abstract—Direct imaging of exoplanets is a challenging task

due to the small angular distance and high contrast relative to

their host star, and the presence of quasi-static noise. We propose

a new statistical method for direct imaging of exoplanets based

on a likelihood ratio detection map, which assumes that the noise

after the background subtraction step obeys a Laplacian distri-

bution. We compare the method with two detection approaches

based on signal-to-noise ratio (SNR) map after performing the

background subtraction by the widely used Annular Principal

Component Analysis (AnnPCA). The experimental results on the

Beta Pictoris data set show the method outperforms SNR maps

in terms of achieving the highest true positive rate (TPR) at zero

false positive rate (FPR).

Index Terms—exoplanet detection, direct imaging, angular dif-

ferential imaging, maximum likelihood, detection map, likelihood

ratio

I. INTRODUCTION

Out of the nearly 5000 exoplanets that have been discovered,

most of them in recent years, only around a tenth have been

detected by methods of direct imaging, that is, based on

the faint light they emit [1]. In fact, the existence of most

of the exoplanets is veriﬁed by indirect imaging methods

based on measuring the effect a planet has on the starlight

reaching Earth, such as when the planet blocks the light of

the star, called the transit method. However, indirect methods

are limited to a speciﬁc alignment between the planet, the star,

and the observer, and biased towards close and massive planets

orbiting old quiet stars.

Directly imaging an exoplanet is a challenging task due to

the light emitted by the planet being very faint and its resolu-

tion being very small, especially compared to the light emitted

by the nearby star, referred to as the host. This motivates the

need for telescopes capable of both high resolution and high

contrast, which due to physical constraints, are limited to being

ground-based rather than space-based. Consequently, the im-

ages obtained by the ground-based telescopes are deformed by

This work was supported by the Fonds de la Recherche Scientiﬁque - FNRS

and the Fonds Wetenschappelijk Onderzoek - Vlaanderen under EOS Project

no. 30468160. Simon Vary is a beneﬁciary of the FSR Incoming Post-doctoral

Fellowship.

the atmospheric turbulence and other instrumental aberrations

of the optics resulting in high-intensity noise called quasi-

static speckles, whose shape and intensity are inconveniently

similar to the planet companions we are trying to ﬁnd.

Angular differential imaging (ADI) partially overcomes the

problem of quasi-static speckles by taking a sequence of im-

ages of a target star over a single night of observation without

compensating for the Earth’s rotation [2]. As a result, potential

planet companions end up following circular trajectories across

the image sequence, while the star and its quasi-static speckle

ﬁeld, being almost ﬁxed with respect to the pupil of the

telescope, remain roughly in the same location, exposing the

detection problem to the use of dynamic-foreground/static-

background separation methods [3].

The complete pipeline of ADI detection consists of three

steps. The ﬁrst is the background subtraction, which estimates

the model PSF containing the speckles and the residual cube

that is meant to contain only the planets and some residual

noise. The standard and most widely used methods are based

on low-rank matrix models, such as principal component

analysis (PCA) [4], [5], its annular version (AnnPCA) [6], and

the low-rank plus sparse method (LLSG) [7]. The rationale

behind the low-rank models is that the bright, quasi-static

speckles are captured by the ﬁrst few principal components,

while the higher-rank moving planets are excluded from the

model. Other methods are based on a maximum likelihood

approach [8] or supervised machine learning methods [9].

The second step is the ﬂux estimation of the residual cube,

in which we, under some probabilistic model, compute the

ﬂux, i.e. the estimated light intensity of the planet, for each

postulated planet trajectory. Classical approaches are median-

based [2] and likelihood based [10], [11].

The ﬁnal third step is to compute the detection map for

the image, which assigns a value to every pixel indicating

how much we believe a planet is located in the pixel. From

the detection map, pixels can then be predicted positive or

negative according to whether the value is above or below

a detection threshold. A common detection map based on

arXiv:2210.10609v1 [astro-ph.IM] 19 Oct 2022

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LikelihoodratiomapfordirectexoplanetdetectionHazanDaglayanICTEAMInstituteUCLouvainLouvain-la-Neuve,Belgiumhazan.daglayan@uclouvain.beSimonVaryICTEAMInstituteUCLouvainLouvain-la-Neuve,Belgiumsimon.vary@uclouvain.beFaustineCantalloubeCNRS,CNES,LAMAixMarseilleUnivMarseille,Francefaustine.cantalloube@la...

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Likelihood ratio map for direct exoplanet detection Hazan Daglayan ICTEAM Institute

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