1,001 research outputs found
Closure statistics in interferometric data
Interferometric visibilities, reflecting the complex correlations between
signals recorded at antennas in an interferometric array, carry information
about the angular structure of a distant source. While unknown antenna gains in
both amplitude and phase can prevent direct interpretation of these
measurements, certain combinations of visibilities called closure phases and
closure amplitudes are independent of antenna gains and provide a convenient
set of robust observables. However, these closure quantities have subtle noise
properties and are generally both linearly and statistically dependent. These
complications have obstructed the proper use of closure quantities in
interferometric analysis, and they have obscured the relationship between
analysis with closure quantities and other analysis techniques such as self
calibration. We review the statistics of closure quantities, noting common
pitfalls that arise when approaching low signal-to-noise due to the nonlinear
propagation of statistical errors. We then develop a strategy for isolating and
fitting to the independent degrees of freedom captured by the closure
quantities through explicit construction of linearly independent sets of
quantities along with their noise covariance in the Gaussian limit, valid for
moderate signal-to-noise, and we demonstrate that model fits have biased
posteriors when this covariance is ignored. Finally, we introduce a unified
procedure for fitting to both closure information and partially calibrated
visibilities, and we demonstrate both analytically and numerically the direct
equivalence of inference based on closure quantities to that based on self
calibration of complex visibilities with unconstrained antenna gains.Comment: 31 pages, 17 figure
Recommended from our members
Multiscale wavelet representations for mammographic feature analysis
This paper introduces a novel approach for accomplishing mammographic feature analysis through multiresolution representations. We show that efficient (nonredundant) representations may be identified from digital mammography and used to enhance specific mammographic features within a continuum of scale space. The multiresolution decomposition of wavelet transforms provides a natural hierarchy in which to embed an interactive paradigm for accomplishing scale space feature analysis. Choosing wavelets (or analyzing functions) that are simultaneously localized in both space and frequency, results in a powerful methodology for image analysis. Multiresolution and orientation selectivity, known biological mechanisms in primate vision, are ingrained in wavelet representations and inspire the techniques presented in this paper. Our approach includes local analysis of complete multiscale representations. Mammograms are reconstructed from wavelet coefficients, enhanced by linear, exponential and constant weight functions localized in scale space. By improving the visualization of breast pathology we can improve the changes of early detection of breast cancers (improve quality) while requiring less time to evaluate mammograms for most patients (lower costs)
Visual Reference and Iconic Content
Evidence from cognitive science supports the claim that humans and other animals see the world as divided into objects. Although this claim is widely accepted, it remains unclear whether the mechanisms of visual reference have representational content or are directly instantiated in the functional architecture. I put forward a version of the former approach that construes object files as icons for objects. This view is consistent with the evidence that motivates the architectural account, can respond to the key arguments against representational accounts, and has explanatory advantages. I draw general lessons for the philosophy of perception and the naturalization of intentionality
A Formal Framework for Speedup Learning from Problems and Solutions
Speedup learning seeks to improve the computational efficiency of problem
solving with experience. In this paper, we develop a formal framework for
learning efficient problem solving from random problems and their solutions. We
apply this framework to two different representations of learned knowledge,
namely control rules and macro-operators, and prove theorems that identify
sufficient conditions for learning in each representation. Our proofs are
constructive in that they are accompanied with learning algorithms. Our
framework captures both empirical and explanation-based speedup learning in a
unified fashion. We illustrate our framework with implementations in two
domains: symbolic integration and Eight Puzzle. This work integrates many
strands of experimental and theoretical work in machine learning, including
empirical learning of control rules, macro-operator learning, Explanation-Based
Learning (EBL), and Probably Approximately Correct (PAC) Learning.Comment: See http://www.jair.org/ for any accompanying file
Application of Nonredundant Sampling Representations of Electromagnetic Fields to NF-FF Transformation Techniques
An overview of the application of the band-limitation properties and nonredundant sampling representations of electromagnetic fields to NF-FF transformations is presented. The progresses achieved by applying them to data acquired on conventional NF scanning surfaces are discussed, outlining the remarkable reduction in the number of needed NF samples and measurement time. An optimal sampling interpolation expansion for reconstructing the probe response on a rotational scanning surface from a non-redundant number of its samples is also discussed. A unified theory of the NF-FF transformations with spiral scannings, which allow a remarkable reduction of the measurement time, is then reviewed by describing a sampling representation of the voltage on a quite arbitrary rotational surface from its nonredundant samples collected on a proper spiral wrapping it. Some numerical and experimental results assessing the effectiveness of the considered NF-FF transformations are shown too
Sparse Signal Separation in Redundant Dictionaries
We formulate a unified framework for the separation of signals that are
sparse in "morphologically" different redundant dictionaries. This formulation
incorporates the so-called "analysis" and "synthesis" approaches as special
cases and contains novel hybrid setups. We find corresponding coherence-based
recovery guarantees for an l1-norm based separation algorithm. Our results
recover those reported in Studer and Baraniuk, ACHA, submitted, for the
synthesis setting, provide new recovery guarantees for the analysis setting,
and form a basis for comparing performance in the analysis and synthesis
settings. As an aside our findings complement the D-RIP recovery results
reported in Cand\`es et al., ACHA, 2011, for the "analysis" signal recovery
problem: minimize_x ||{\Psi}x||_1 subject to ||y - Ax||_2 \leq {\epsilon}, by
delivering corresponding coherence-based recovery results.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT),
Boston, MA, July 201
Optical aperture synthetic images of the photosphere and molecular atmosphere of Mira
We have used aperture synthetic imaging methods to obtain diffraction-limited images of the photosphere and molecular atmosphere of the long period variable star Mira (o Ceti). These maps, obtained close to the peak of Mira's variability cycle, clearly indicate substantial distortions from circular symmetry. Our image of the emission due to resonant scattering of TiO shows a significant contribution due to a cool atmosphere with a radius one and a half times as great as that of the photosphere. We suggest that the photospheric asymmetry is most likely associated with the intrinsic pulsation mode of the star and that stable nonradial pulsation modes can coexist with the radial modes that are responsible for the photometric variability. Further aperture synthetic mapping, which should be possible for a major fraction of the photometric cycle, is capable of verifying this hypothesis
Nonhomogeneous Wavelet Systems in High Dimensions
It is of interest to study a wavelet system with a minimum number of
generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in
[11] that for any real-valued expansive matrix M, a homogeneous
orthonormal M-wavelet basis can be generated by a single wavelet function. On
the other hand, it has been demonstrated in [21] that nonhomogeneous wavelet
systems, though much less studied in the literature, play a fundamental role in
wavelet analysis and naturally link many aspects of wavelet analysis together.
In this paper, we are interested in nonhomogeneous wavelet systems in high
dimensions with a minimum number of generators. As we shall see in this paper,
a nonhomogeneous wavelet system naturally leads to a homogeneous wavelet system
with almost all properties preserved. We also show that a nonredundant
nonhomogeneous wavelet system is naturally connected to refinable structures
and has a fixed number of wavelet generators. Consequently, it is often
impossible for a nonhomogeneous orthonormal wavelet basis to have a single
wavelet generator. However, for redundant nonhomogeneous wavelet systems, we
show that for any real-valued expansive matrix M, we can always
construct a nonhomogeneous smooth tight M-wavelet frame in with a
single wavelet generator whose Fourier transform is a compactly supported
function. Moreover, such nonhomogeneous tight wavelet frames are
associated with filter banks and can be modified to achieve directionality in
high dimensions. Our analysis of nonhomogeneous wavelet systems employs a
notion of frequency-based nonhomogeneous wavelet systems in the distribution
space. Such a notion allows us to separate the perfect reconstruction property
of a wavelet system from its stability in function spaces
Dual Descriptions of SO(10) SUSY Gauge Theories with Arbitrary Numbers of Spinors and Vectors
We examine the low energy structure of N=1 supersymmetric SO(10) gauge theory
with matter chiral superfields in N_Q spinor and N_f vector representations. We
construct a dual to this model based upon an SU(N_f+2N_Q-7) x Sp(2N_Q-2) gauge
group without utilizing deconfinement methods. This product theory generalizes
all previously known Pouliot-type duals to SO(N_c) models with spinor and
vector matter. It also yields large numbers of new dual pairs along various
flat directions. The dual description of the SO(10) theory satisfies multiple
consistency checks including an intricate renormalization group flow analysis
which links it with Seiberg's duality transformations. We discuss its
implications for building grand unified theories that contain all Standard
Model fields as composite degrees of freedom.Comment: 36 pages, harvmac and tables macros, 1 figur
- …