Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods break down in presence of high coherence and large noise. We propose a new regularization approach to handle model collinearity and obtain parsimonious frequency selection simultaneously. It takes advantage of the pairing structure of sine and cosine atoms in the frequency dictionary. A probabilistic spectrum screening is also developed for fast computation in high dimensions. A data-resampling version of high-dimensional Bayesian Information Criterion is used to determine the regularization parameters. Experiments show the efficacy and efficiency of the proposed algorithms in challenging situations with small sample size, high frequency resolution, and low signal-to-noise ratio

LSDCat: Detection and cataloguing of emission-line sources in integral-field spectroscopy datacubes

We present a robust, efficient, and user-friendly algorithm for detecting faint emission-line sources in large integral-field spectroscopic datacubes together with the public release of the software package LSDCat (Line Source Detection and Cataloguing). LSDCat uses a 3-dimensional matched filter approach, combined with thresholding in signal-to-noise, to build a catalogue of individual line detections. In a second pass, the detected lines are grouped into distinct objects, and positions, spatial extents, and fluxes of the detected lines are determined. LSDCat requires only a small number of input parameters, and we provide guidelines for choosing appropriate values. The software is coded in Python and capable to process very large datacubes in a short time. We verify the implementation with a source insertion and recovery experiment utilising a real datacube taken with the MUSE instrument at the ESO Very Large Telescope.Comment: 14 pages. Accepted for publication in Astronomy & Astrophysics. The LSDCat software is available at https://bitbucket.org/Knusper2000/lsdcat, v2 corrected typos and language editin

Stable Recovery Of Sparse Vectors From Random Sinusoidal Feature Maps

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical analysis shows that collecting a sufficient number of such features can be reliably used for subsequent inference in kernel classification and regression. In this work, we demonstrate that with a mild increase in the dimension of the embedding, it is also possible to reconstruct the data vector from such random sinusoidal features, provided that the underlying data is sparse enough. In particular, we propose a numerically stable algorithm for reconstructing the data vector given the nonlinear features, and analyze its sample complexity. Our algorithm can be extended to other types of structured inverse problems, such as demixing a pair of sparse (but incoherent) vectors. We support the efficacy of our approach via numerical experiments

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

The MUSE-Wide Survey: A first catalogue of 831 emission line galaxies

We present a first instalment of the MUSE-Wide survey, covering an area of 22.2 arcmin$^2$ (corresponding to $\sim$20% of the final survey) in the CANDELS/Deep area of the Chandra Deep Field South. We use the MUSE integral field spectrograph at the ESO VLT to conduct a full-area spectroscopic mapping at a depth of 1h exposure time per 1 arcmin$^2$ pointing. We searched for compact emission line objects using our newly developed LSDCat software based on a 3-D matched filtering approach, followed by interactive classification and redshift measurement of the sources. Our catalogue contains 831 distinct emission line galaxies with redshifts ranging from 0.04 to 6. Roughly one third (237) of the emission line sources are Lyman $\alpha$ emitting galaxies with $3 < z < 6$, only four of which had previously measured spectroscopic redshifts. At lower redshifts 351 galaxies are detected primarily by their [OII] emission line ($0.3 \lesssim z \lesssim 1.5$), 189 by their [OIII] line ($0.21 \lesssim z \lesssim 0.85$), and 46 by their H$\alpha$ line ($0.04 \lesssim z \lesssim 0.42$). Comparing our spectroscopic redshifts to photometric redshift estimates from the literature, we find excellent agreement for $z<1.5$ with a median $\Delta z$ of only $\sim 4 \times 10^{-4}$ and an outlier rate of 6%, however a significant systematic offset of $\Delta z = 0.26$ and an outlier rate of 23% for Ly$\alpha$ emitters at $z>3$. Together with the catalogue we also release 1D PSF-weighted extracted spectra and small 3D datacubes centred on each of the 831 sources.Comment: 24 pages, 14 figures, accepted for publication in A&A, data products are available for download from http://muse-vlt.eu/science/muse-wide-survey/ and later via the CD