7,101 research outputs found
Quantitative analysis of the reconstruction performance of interpolants
The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed
Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems
This paper deals with the resolution of inverse problems in a periodic
setting or, in other terms, the reconstruction of periodic continuous-domain
signals from their noisy measurements. We focus on two reconstruction
paradigms: variational and statistical. In the variational approach, the
reconstructed signal is solution to an optimization problem that establishes a
tradeoff between fidelity to the data and smoothness conditions via a quadratic
regularization associated to a linear operator. In the statistical approach,
the signal is modeled as a stationary random process defined from a Gaussian
white noise and a whitening operator; one then looks for the optimal estimator
in the mean-square sense. We give a generic form of the reconstructed signals
for both approaches, allowing for a rigorous comparison of the two.We fully
characterize the conditions under which the two formulations yield the same
solution, which is a periodic spline in the case of sampling measurements. We
also show that this equivalence between the two approaches remains valid on
simulations for a broad class of problems. This extends the practical range of
applicability of the variational method
Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions
An algorithm for fast calculation of the Coulombic forces and energies of
point particles with free boundary conditions is proposed. Its calculation time
scales as N log N for N particles. This novel method has lower crossover point
with the full O(N^2) direct summation than the Fast Multipole Method. The
forces obtained by our algorithm are analytical derivatives of the energy which
guarantees energy conservation during a molecular dynamics simulation. Our
algorithm is very simple. An MPI parallelised version of the code can be
downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic
How to mesh up Ewald sums (I): A theoretical and numerical comparison of various particle mesh routines
Standard Ewald sums, which calculate e.g. the electrostatic energy or the
force in periodically closed systems of charged particles, can be efficiently
speeded up by the use of the Fast Fourier Transformation (FFT). In this article
we investigate three algorithms for the FFT-accelerated Ewald sum, which
attracted a widespread attention, namely, the so-called
particle-particle-particle-mesh (P3M), particle mesh Ewald (PME) and smooth PME
method. We present a unified view of the underlying techniques and the various
ingredients which comprise those routines. Additionally, we offer detailed
accuracy measurements, which shed some light on the influence of several tuning
parameters and also show that the existing methods -- although similar in
spirit -- exhibit remarkable differences in accuracy. We propose combinations
of the individual components, mostly relying on the P3M approach, which we
regard as most flexible.Comment: 18 pages, 8 figures included, revtex styl
Concepts for on-board satellite image registration, volume 1
The NASA-NEEDS program goals present a requirement for on-board signal processing to achieve user-compatible, information-adaptive data acquisition. One very specific area of interest is the preprocessing required to register imaging sensor data which have been distorted by anomalies in subsatellite-point position and/or attitude control. The concepts and considerations involved in using state-of-the-art positioning systems such as the Global Positioning System (GPS) in concert with state-of-the-art attitude stabilization and/or determination systems to provide the required registration accuracy are discussed with emphasis on assessing the accuracy to which a given image picture element can be located and identified, determining those algorithms required to augment the registration procedure and evaluating the technology impact on performing these procedures on-board the satellite
The Panchromatic High-Resolution Spectroscopic Survey of Local Group Star Clusters - I. General Data Reduction Procedures for the VLT/X-shooter UVB and VIS arm
Our dataset contains spectroscopic observations of 29 globular clusters in
the Magellanic Clouds and the Milky Way performed with VLT/X-shooter. Here we
present detailed data reduction procedures for the VLT/X-shooter UVB and VIS
arm. These are not restricted to our particular dataset, but are generally
applicable to different kinds of X-shooter data without major limitation on the
astronomical object of interest. ESO's X-shooter pipeline (v1.5.0) performs
well and reliably for the wavelength calibration and the associated
rectification procedure, yet we find several weaknesses in the reduction
cascade that are addressed with additional calibration steps, such as bad pixel
interpolation, flat fielding, and slit illumination corrections. Furthermore,
the instrumental PSF is analytically modeled and used to reconstruct flux
losses at slit transit and for optimally extracting point sources. Regular
observations of spectrophotometric standard stars allow us to detect
instrumental variability, which needs to be understood if a reliable absolute
flux calibration is desired. A cascade of additional custom calibration steps
is presented that allows for an absolute flux calibration uncertainty of less
than ten percent under virtually every observational setup provided that the
signal-to-noise ratio is sufficiently high. The optimal extraction increases
the signal-to-noise ratio typically by a factor of 1.5, while simultaneously
correcting for resulting flux losses. The wavelength calibration is found to be
accurate to an uncertainty level of approximately 0.02 Angstrom. We find that
most of the X-shooter systematics can be reliably modeled and corrected for.
This offers the possibility of comparing observations on different nights and
with different telescope pointings and instrumental setups, thereby
facilitating a robust statistical analysis of large datasets.Comment: 22 pages, 18 figures, Accepted for publication in Astronomy &
Astrophysics; V2 contains a minor change in the abstract. We note that we did
not test X-shooter pipeline versions 2.0 or later. V3 contains an updated
referenc
- …