Parametric spectral analysis: scale and shift

We introduce the paradigm of dilation and translation for use in the spectral analysis of complex-valued univariate or multivariate data. The new procedure stems from a search on how to solve ambiguity problems in this analysis, such as aliasing because of too coarsely sampled data, or collisions in projected data, which may be solved by a translation of the sampling locations. In Section 2 both dilation and translation are first presented for the classical one-dimensional exponential analysis. In the subsequent Sections 3--7 the paradigm is extended to more functions, among which the trigonometric functions cosine, sine, the hyperbolic cosine and sine functions, the Chebyshev and spread polynomials, the sinc, gamma and Gaussian function, and several multivariate versions of all of the above. Each of these function classes needs a tailored approach, making optimal use of the properties of the base function used in the considered sparse interpolation problem. With each of the extensions a structured linear matrix pencil is associated, immediately leading to a computational scheme for the spectral analysis, involving a generalized eigenvalue problem and several structured linear systems. In Section 8 we illustrate the new methods in several examples: fixed width Gaussian distribution fitting, sparse cardinal sine or sinc interpolation, and lacunary or supersparse Chebyshev polynomial interpolation

Constructing A Flexible Likelihood Function For Spectroscopic Inference

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. For the high signal-to-noise data with large spectral range that is commonly employed in stellar astrophysics, that covariant structure can lead to dramatically underestimated parameter uncertainties (and, in some cases, biases). We construct a likelihood function that accounts for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. This framework specifically address the common problem of mismatches in model spectral line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic/molecular databases or opacity prescriptions) by developing a novel local covariance kernel formalism that identifies and self-consistently downweights pathological spectral line "outliers." By fitting many spectra in a hierarchical manner, these local kernels provide a mechanism to learn about and build data-driven corrections to synthetic spectral libraries. An open-source software implementation of this approach is available at http://iancze.github.io/Starfish, including a sophisticated probabilistic scheme for spectral interpolation when using model libraries that are sparsely sampled in the stellar parameters. We demonstrate some salient features of the framework by fitting the high resolution $V$-band spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate resolution $K$-band spectrum of Gliese 51, an M5 field dwarf.Comment: Accepted to ApJ. Incorporated referees' comments. New figures 1, 8, 10, 12, and 14. Supplemental website: http://iancze.github.io/Starfish

Joint Demosaicing and Super-Resolution Imaging from a Set of Unregistered Aliased Images

We present a new algorithm that performs demosaicing and super-resolution jointly from a set of raw images sampled with a color filter array. Such a combined approach allows us to compute the alignment parameters between the images on the raw camera data before interpolation artifacts are introduced. After image registration, a high resolution color image is reconstructed at once using the full set of images. For this, we use normalized convolution, an image interpolation method from a nonuniform set of samples. Our algorithm is tested and compared to other approaches in simulations and practical experiments

The SAMI Galaxy Survey: Cubism and covariance, putting round pegs into square holes

We present a methodology for the regularization and combination of sparse sampled and irregularly gridded observations from fibre-optic multiobject integral field spectroscopy. The approach minimizes interpolation and retains image resolution on combining subpixel dithered data. We discuss the methodology in the context of the Sydney-AAO multiobject integral field spectrograph (SAMI) Galaxy Survey underway at the Anglo-Australian Telescope. The SAMI instrument uses 13 fibre bundles to perform high-multiplex integral field spectroscopy across a 1° diameter field of view. The SAMI Galaxy Survey is targeting ~3000 galaxies drawn from the full range of galaxy environments. We demonstrate the subcritical sampling of the seeing and incomplete fill factor for the integral field bundles results in only a 10 per cent degradation in the final image resolution recovered. We also implement a new methodology for tracking covariance between elements of the resulting data cubes which retains 90 per cent of the covariance information while incurring only a modest increase in the survey data volume

Continuous Plasma density measurement in TJ-II infrared interferometer-Advanced signal processing based on FPGAs

This work presents the behavioral simulation in an FPGA of a novel processing system for measuring line average electronic density in the TJ-II stellarator diagnostic, Infra-Red Two-Color Interferometer. Line average electronic density is proportional to phase difference between probing and reference signals of the interferometer, as the Appleton–Hartree cold plasma model states. The novelty of the approach is the development of a real time measuring system where research work has been carried out in two ways: a new interpolation algorithm and the implementation of a new specific processor on an FPGA. The main goal of this new system is to measure line plasma electronic density for several channels in real time, also it will be useful to eliminate intermediate mixing frequency stages (the output signals coming from the interferometer are going to be directly sampled) and finally to generate real time density signals for control purposes in TJ-II and in other diagnostics. This device is intended to be the new data acquisition-processing system for the future six channel infrared interferometer that requires at least 14 input signals. The knowledge acquired could be useful in the design of W7-X and ITER IR-interferometer data acquisition and processing systems

TESTING THE PERFORMANCE OF DIFFERENT SPATIAL INTERPOLATION TECHNIQUES ON MAPPING SHORT DATASERIES OF PRECIPITATION PROPRETIES

patial interpolation, in the context of spatial analysis, can be defined as the derivation of new data from already known information, a technique frequently used to predict and quantify spatial variation of a certain property or parameter. In this study we compared the performance of Inverse Distance Weighted (IDW), Ordinary Kriging and Natural Neighbor techniques, applied in spatial interpolation of precipitation parameters (pH, electrical conductivity and total dissolved solids). These techniques are often used when the area of interest is relatively small and the sampled locations are regularly spaced. The methods were tested on data collected in Iasi city (Romania) between March – May 2013. Spatial modeling was performed on a small dataset, consisting of 7 sample locations and 13 different known values of each analyzed parameter. The precision of the techniques used is directly dependent on sample density as well as data variation, greater fluctuations in values between locations causing a decrease in the accuracy of the methods used. To validate the results and reveal the best method of interpolating rainfall characteristics, leave-one – out cross-validation approach was used. Comparing residues between the known values and the estimated values of pH, electrical conductivity and total dissolved solids, it was revealed that Natural Neighbor stands out as generating the smallest residues for pH and electrical conductivity, whereas IDW presents the smallest error in interpolating total dissolved solids (the parameter with the highest fluctuations in value)