Low-rank plus sparse decomposition for exoplanet detection in direct-imaging ADI sequences

The LLSG algorithm

¹ Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du Six Août 19c, 4000 Liège, Belgium
e-mail: cgomez@ulg.ac.be
² Department of Mathematical Engineering, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
³ Montefiore Institute, Université de Liège, 4000 Liège, Belgium
⁴ Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA

Received: 17 September 2015
Accepted: 20 January 2016

Abstract

Context. Data processing constitutes a critical component of high-contrast exoplanet imaging. Its role is almost as important as the choice of a coronagraph or a wavefront control system, and it is intertwined with the chosen observing strategy. Among the data processing techniques for angular differential imaging (ADI), the most recent is the family of principal component analysis (PCA) based algorithms. It is a widely used statistical tool developed during the first half of the past century. PCA serves, in this case, as a subspace projection technique for constructing a reference point spread function (PSF) that can be subtracted from the science data for boosting the detectability of potential companions present in the data. Unfortunately, when building this reference PSF from the science data itself, PCA comes with certain limitations such as the sensitivity of the lower dimensional orthogonal subspace to non-Gaussian noise.

Aims. Inspired by recent advances in machine learning algorithms such as robust PCA, we aim to propose a localized subspace projection technique that surpasses current PCA-based post-processing algorithms in terms of the detectability of companions at near real-time speed, a quality that will be useful for future direct imaging surveys.

Methods. We used randomized low-rank approximation methods recently proposed in the machine learning literature, coupled with entry-wise thresholding to decompose an ADI image sequence locally into low-rank, sparse, and Gaussian noise components (LLSG). This local three-term decomposition separates the starlight and the associated speckle noise from the planetary signal, which mostly remains in the sparse term. We tested the performance of our new algorithm on a long ADI sequence obtained on β Pictoris with VLT/NACO.

Results. Compared to a standard PCA approach, LLSG decomposition reaches a higher signal-to-noise ratio and has an overall better performance in the receiver operating characteristic space. This three-term decomposition brings a detectability boost compared to the full-frame standard PCA approach, especially in the small inner working angle region where complex speckle noise prevents PCA from discerning true companions from noise.