Related papers: An Alternating Minimization Algorithm with Traject…
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…
We propose an algorithm for the Wireless Sensor Network localization problem, which is based on the well-known algorithmic framework of Alternating Minimization. We start with a non-smooth and non-convex minimization, and transform it into…
We present a new matched filter algorithm for direct detection of point sources in the immediate vicinity of bright stars. The stellar Point Spread Function (PSF) is first subtracted using a Karhunen-Lo\'eve Image Processing (KLIP)…
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
Among the group of extrasolar planets, transiting planets provide a great opportunity to obtain direct measurements for the basic physical properties, such as mass and radius of these objects. These planets are therefore highly important in…
Today's most detailed characterization of exoplanet atmospheres is accessible via transit spectroscopy (TS). Detecting transiting exoplanets only yields their size, and it is thus standard to measure a planet's mass before moving towards…
The detection of periodic signals from transiting exoplanets is often impeded by extraneous aperiodic photometric variability, either intrinsic to the star or arising from the measurement process. Frequently, these variations are…
In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the…
The minimum action method (MAM) is to calculate the most probable transition path in randomly perturbed stochastic dynamics, based on the idea of action minimization in the path space. The accuracy of the numerical path between different…
(abridged) The technique of gravitational microlensing is currently unique in its ability to provide a sample of terrestrial exoplanets around both Galactic disk and bulge stars, allowing to measure their abundance and determine their…
The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
In this paper, we propose a novel element-wise subset selection method for the alternating least squares (ALS) algorithm, focusing on low-rank matrix factorization involving matrices with missing values, as commonly encountered in…
This study explores the application of autoencoder-based machine learning techniques for anomaly detection to identify exoplanet atmospheres with unconventional chemical signatures using a low-dimensional data representation. We use the…
Initially designed to detect and characterize exoplanets, extreme adaptive optics systems (AO) open a new window on the solar system by resolving its small bodies. Nonetheless, despite the always increasing performances of AO systems, the…
We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve…
A new generation of telescopes with mirror diameters of 20 m or more, called extremely large telescopes (ELTs) has the potential to provide unprecedented imaging and spectroscopy of exo-planetary systems, if the difficulties in achieving…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…
The approximation of tensors has important applications in various disciplines, but it remains an extremely challenging task. It is well known that tensors of higher order can fail to have best low-rank approximations, but with an important…