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

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.

Observing Exoplanets with High Dispersion Coronagraphy. I. The Scientific Potential of Current and Next-generation Large Ground and Space Telescopes

“…This operation was successfully carried out in 2015 and is now available to the Keck community in shared-risk mode. The upgrade not only came with a brand-new coronagraph focal plane mask, but also a suite of software packages to automate the coronagraph acquisition procedure, including automatic ultraprecise centering (Huby et al 2015), speckle nulling wavefront control (Bottom et al 2016), and an open-source python-based data reduction package (Gomez Gonzalez et al 2016). The second upgrade component is an infrared pyramid wavefront sensor demonstration, and a potential facility for the Keck II AOs system.…”

VIP: Vortex Image Processing Package for High-contrast Direct Imaging

“…For aplanet S/N calculation, we implement the small sample statistics approach proposed by Mawet et al (2014), which uses a two-sample t-test with statistics computed over resolution elements (circular apertures of D l diameter) instead of considering the pixels as statistically independent (Mawet et al 2014;Gomez Gonzalez et al 2016a). The subpackage stats contains functions for computing statistics from regions of frames or cubes, sigma filtering of pixels in frames, and for computing distance and correlation measures between frames.…”

“…ADI can be paired with several post-processing algorithms, such as the least-squares based LOCI (locally optimized combination of images, Lafrenière et al 2007), the maximum likelihood based ANDROMEDA (Mugnier et al 2009;Cantalloube et al 2015), and the family of principal component analysis (PCA) based algorithms (Amara & Quanz 2012;Soummer et al 2012). Recent algorithms such as LLSG (Gomez Gonzalez et al 2016a) aim to decompose the images into lowrank, sparse, and Gaussian-noise terms in order to separate the companion signal from the star point-spread function (PSF) and speckle field. A common step in any of these approaches is the use of a model PSF.…”

Precise radial velocities of giant stars

“…As an alternative to the standard PCA, we also used the new algorithm recently introduced by Gomez Gonzalez et al (2016b) to subtract the stellar PSF of high-contrast images and enhance the signal of faint companions. The method is named by the authors local low-rank plus sparse plus Gaussian-noise decomposition (LLSG).…”