1,611 research outputs found
Selective Principal Component Extraction and Reconstruction: A Novel Method for Ground Based Exoplanet Spectroscopy
Context: Infrared spectroscopy of primary and secondary eclipse events probes
the composition of exoplanet atmospheres and, using space telescopes, has
detected H2O, CH4 and CO2 in three hot Jupiters. However, the available data
from space telescopes has limited spectral resolution and does not cover the
2.4 - 5.2 micron spectral region. While large ground based telescopes have the
potential to obtain molecular-abundance-grade spectra for many exoplanets,
realizing this potential requires retrieving the astrophysical signal in the
presence of large Earth-atmospheric and instrument systematic errors. Aims:
Here we report a wavelet-assisted, selective principal component extraction
method for ground based retrieval of the dayside spectrum of HD 189733b from
data containing systematic errors. Methods: The method uses singular value
decomposition and extracts those critical points of the Rayleigh quotient which
correspond to the planet induced signal. The method does not require prior
knowledge of the planet spectrum or the physical mechanisms causing systematic
errors. Results: The spectrum obtained with our method is in excellent
agreement with space based measurements made with HST and Spitzer (Swain et al.
2009b; Charbonneau et al. 2008) and confirms the recent ground based
measurements (Swain et al. 2010) including the strong 3.3 micron emission.Comment: 4 pages, 3 figures; excepted for publication by A&
Analysis of Basis Pursuit Via Capacity Sets
Finding the sparsest solution for an under-determined linear system
of equations is of interest in many applications. This problem is
known to be NP-hard. Recent work studied conditions on the support size of
that allow its recovery using L1-minimization, via the Basis Pursuit
algorithm. These conditions are often relying on a scalar property of
called the mutual-coherence. In this work we introduce an alternative set of
features of an arbitrarily given , called the "capacity sets". We show how
those could be used to analyze the performance of the basis pursuit, leading to
improved bounds and predictions of performance. Both theoretical and numerical
methods are presented, all using the capacity values, and shown to lead to
improved assessments of the basis pursuit success in finding the sparest
solution of
Spin-lattice Interaction in Ruby Measured by ESR in Uniaxially Stressed Crystals
Spin-lattice Hamiltonian determined for chromium ions in ruby single crystal
Blind Deconvolution of Ultrasonic Signals Using High-Order Spectral Analysis and Wavelets
Defect detection by ultrasonic method is limited by the pulse width.
Resolution can be improved through a deconvolution process with a priori
information of the pulse or by its estimation. In this paper a regularization
of the Wiener filter using wavelet shrinkage is presented for the estimation of
the reflectivity function. The final result shows an improved signal to noise
ratio with better axial resolution.Comment: 8 pages, CIARP 2005, LNCS 377
Bi-stochastic kernels via asymmetric affinity functions
In this short letter we present the construction of a bi-stochastic kernel p
for an arbitrary data set X that is derived from an asymmetric affinity
function {\alpha}. The affinity function {\alpha} measures the similarity
between points in X and some reference set Y. Unlike other methods that
construct bi-stochastic kernels via some convergent iteration process or
through solving an optimization problem, the construction presented here is
quite simple. Furthermore, it can be viewed through the lens of out of sample
extensions, making it useful for massive data sets.Comment: 5 pages. v2: Expanded upon the first paragraph of subsection 2.1. v3:
Minor changes and edits. v4: Edited comments and added DO
Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints
Regularization of ill-posed linear inverse problems via penalization
has been proposed for cases where the solution is known to be (almost) sparse.
One way to obtain the minimizer of such an penalized functional is via
an iterative soft-thresholding algorithm. We propose an alternative
implementation to -constraints, using a gradient method, with
projection on -balls. The corresponding algorithm uses again iterative
soft-thresholding, now with a variable thresholding parameter. We also propose
accelerated versions of this iterative method, using ingredients of the
(linear) steepest descent method. We prove convergence in norm for one of these
projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page
Necessary and sufficient conditions of solution uniqueness in minimization
This paper shows that the solutions to various convex minimization
problems are \emph{unique} if and only if a common set of conditions are
satisfied. This result applies broadly to the basis pursuit model, basis
pursuit denoising model, Lasso model, as well as other models that
either minimize or impose the constraint , where
is a strictly convex function. For these models, this paper proves that,
given a solution and defining I=\supp(x^*) and s=\sign(x^*_I),
is the unique solution if and only if has full column rank and there
exists such that and for . This
condition is previously known to be sufficient for the basis pursuit model to
have a unique solution supported on . Indeed, it is also necessary, and
applies to a variety of other models. The paper also discusses ways to
recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte
On Verifiable Sufficient Conditions for Sparse Signal Recovery via Minimization
We propose novel necessary and sufficient conditions for a sensing matrix to
be "-good" - to allow for exact -recovery of sparse signals with
nonzero entries when no measurement noise is present. Then we express the error
bounds for imperfect -recovery (nonzero measurement noise, nearly
-sparse signal, near-optimal solution of the optimization problem yielding
the -recovery) in terms of the characteristics underlying these
conditions. Further, we demonstrate (and this is the principal result of the
paper) that these characteristics, although difficult to evaluate, lead to
verifiable sufficient conditions for exact sparse -recovery and to
efficiently computable upper bounds on those for which a given sensing
matrix is -good. We establish also instructive links between our approach
and the basic concepts of the Compressed Sensing theory, like Restricted
Isometry or Restricted Eigenvalue properties
On the performance of algorithms for the minimization of -penalized functionals
The problem of assessing the performance of algorithms used for the
minimization of an -penalized least-squares functional, for a range of
penalty parameters, is investigated. A criterion that uses the idea of
`approximation isochrones' is introduced. Five different iterative minimization
algorithms are tested and compared, as well as two warm-start strategies. Both
well-conditioned and ill-conditioned problems are used in the comparison, and
the contrast between these two categories is highlighted.Comment: 18 pages, 10 figures; v3: expanded version with an additional
synthetic test problem
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