The LIGO observatories detect gravitational waves through monitoring changes in the detectors length down to below $10^{-19}$,$m/sqrt{Hz}$ variation---a small fraction of the size of the atoms that make up the detector. To achieve this sensitivity, t
he detector and its environment need to be closely monitored. Beyond the gravitational wave data stream, LIGO continuously records hundreds of thousands of channels of environmental and instrumental data in order to monitor for possibly minuscule variations that contribute to the detector noise. A particularly challenging issue is the appearance in the gravitational wave signal of brief, loud noise artifacts called ``glitches, which are environmental or instrumental in origin but can mimic true gravitational waves and therefore hinder sensitivity. Currently they are primarily identified by analysis of the gravitational wave data stream. Here we present a machine learning approach that can identify glitches by monitoring textit{all} environmental and detector data channels, a task that has not previously been pursued due to its scale and the number of degrees of freedom within gravitational-wave detectors. The presented method is capable of reducing the gravitational-wave detector networks false alarm rate and improving the LIGO instruments, consequently enhancing detection confidence.
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike sorting, a
nd more. The problem is challenging in both theory and practice, as natural optimization formulations are nonconvex. Moreover, practical deconvolution problems involve smooth motifs (kernels) whose spectra decay rapidly, resulting in poor conditioning and numerical challenges. This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD. This is used to derive a $provable$ algorithm which exactly solves certain non-practical instances of the SaSD problem. We leverage the key ideas from this theory (sphere constraints, data-driven initialization) to develop a $practical$ algorithm, which performs well on data arising from a range of application areas. We highlight key additional challenges posed by the ill-conditioning of real SaSD problems, and suggest heuristics (acceleration, continuation, reweighting) to mitigate them. Experiments demonstrate both the performance and generality of the proposed method.
Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains
a formidable challenge. Fourier analysis is commonly used to analyze the underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of a new algorithm based on nonconvex optimization, applicable to any microscopy modality, that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this novel algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material. Our phase sensitive quasiparticle interference imaging results indicate that the pairing symmetry in optimally doped NaFeAs is consistent with a sign-changing s+- order parameter.
