3,267 research outputs found
Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
Wavelets have been used extensively for several years now in astronomy for
many purposes, ranging from data filtering and deconvolution, to star and
galaxy detection or cosmic ray removal. More recent sparse representations such
ridgelets or curvelets have also been proposed for the detection of anisotropic
features such cosmic strings in the cosmic microwave background.
We review in this paper a range of methods based on sparsity that have been
proposed for astronomical data analysis. We also discuss what is the impact of
Compressed Sensing, the new sampling theory, in astronomy for collecting the
data, transferring them to the earth or reconstructing an image from incomplete
measurements.Comment: Submitted. Full paper will figures available at
http://jstarck.free.fr/IEEE09_SparseAstro.pd
Multiscale likelihood analysis and complexity penalized estimation
We describe here a framework for a certain class of multiscale likelihood
factorizations wherein, in analogy to a wavelet decomposition of an L^2
function, a given likelihood function has an alternative representation as a
product of conditional densities reflecting information in both the data and
the parameter vector localized in position and scale. The framework is
developed as a set of sufficient conditions for the existence of such
factorizations, formulated in analogy to those underlying a standard
multiresolution analysis for wavelets, and hence can be viewed as a
multiresolution analysis for likelihoods. We then consider the use of these
factorizations in the task of nonparametric, complexity penalized likelihood
estimation. We study the risk properties of certain thresholding and
partitioning estimators, and demonstrate their adaptivity and near-optimality,
in a minimax sense over a broad range of function spaces, based on squared
Hellinger distance as a loss function. In particular, our results provide an
illustration of how properties of classical wavelet-based estimators can be
obtained in a single, unified framework that includes models for continuous,
count and categorical data types
A multiresolution framework for local similarity based image denoising
In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise
Adaptive thresholding in dynamic scene analysis for extraction of fine line
This paper presents an adaptive threshold method whereby a fine thin line of one-pixel width lines could be detected in a gray level images. The proposed method uses the percentage difference between the mean of the pixels within a window and the center pixel. The minimum threshold value however is heuristically set to 32. If the percentage difference is greater than 40% then the threshold value will be set to the difference value. This method has been applied in detecting moving objects with fine lines and the results showed that the method was able to pickup straight thin edges that belong to the moving objec
Simulating full-sky interferometric observations
Aperture array interferometers, such as that proposed for the Square
Kilometre Array (SKA), will see the entire sky, hence the standard approach to
simulating visibilities will not be applicable since it relies on a tangent
plane approximation that is valid only for small fields of view. We derive
interferometric formulations in real, spherical harmonic and wavelet space that
include contributions over the entire sky and do not rely on any tangent plane
approximations. A fast wavelet method is developed to simulate the visibilities
observed by an interferometer in the full-sky setting. Computing visibilities
using the fast wavelet method adapts to the sparse representation of the
primary beam and sky intensity in the wavelet basis. Consequently, the fast
wavelet method exhibits superior computational complexity to the real and
spherical harmonic space methods and may be performed at substantially lower
computational cost, while introducing only negligible error to simulated
visibilities. Low-resolution interferometric observations are simulated using
all of the methods to compare their performance, demonstrating that the fast
wavelet method is approximately three times faster that the other methods for
these low-resolution simulations. The computational burden of the real and
spherical harmonic space methods renders these techniques computationally
infeasible for higher resolution simulations. High-resolution interferometric
observations are simulated using the fast wavelet method only, demonstrating
and validating the application of this method to realistic simulations. The
fast wavelet method is estimated to provide a greater than ten-fold reduction
in execution time compared to the other methods for these high-resolution
simulations.Comment: 16 pages, 9 figures, replaced to match version accepted by MNRAS
(major additions to previous version including new fast wavelet method
A robust nonlinear scale space change detection approach for SAR images
In this paper, we propose a change detection approach based on nonlinear scale space analysis of change images for robust detection of various changes incurred by natural phenomena and/or human activities in Synthetic Aperture Radar (SAR) images using Maximally Stable Extremal Regions (MSERs). To achieve this, a variant of the log-ratio image of multitemporal images is calculated which is followed by Feature Preserving Despeckling (FPD) to generate nonlinear scale space images exhibiting different trade-offs in terms of speckle reduction and shape detail preservation. MSERs of each scale space image are found and then combined through a decision level fusion strategy, namely "selective scale fusion" (SSF), where contrast and boundary curvature of each MSER are considered. The performance of the proposed method is evaluated using real multitemporal high resolution TerraSAR-X images and synthetically generated multitemporal images composed of shapes with several orientations, sizes, and backscatter amplitude levels representing a variety of possible signatures of change. One of the main outcomes of this approach is that different objects having different sizes and levels of contrast with their surroundings appear as stable regions at different scale space images thus the fusion of results from scale space images yields a good overall performance
Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope
The multiscale variance stabilization Transform (MSVST) has recently been
proposed for Poisson data denoising. This procedure, which is nonparametric, is
based on thresholding wavelet coefficients. We present in this paper an
extension of the MSVST to 3D data (in fact 2D-1D data) when the third dimension
is not a spatial dimension, but the wavelength, the energy, or the time. We
show that the MSVST can be used for detecting and characterizing astrophysical
sources of high-energy gamma rays, using realistic simulated observations with
the Large Area Telescope (LAT). The LAT was launched in June 2008 on the Fermi
Gamma-ray Space Telescope mission. The MSVST algorithm is very fast relative to
traditional likelihood model fitting, and permits efficient detection across
the time dimension and immediate estimation of spectral properties.
Astrophysical sources of gamma rays, especially active galaxies, are typically
quite variable, and our current work may lead to a reliable method to quickly
characterize the flaring properties of newly-detected sources.Comment: Accepted. Full paper will figures available at
http://jstarck.free.fr/aa08_msvst.pd
Computer vision techniques for forest fire perception
This paper presents computer vision techniques for forest fire perception involving measurement of forest fire properties (fire front, flame height, flame inclination angle, fire base width) required for the implementation of advanced forest fire-fighting strategies. The system computes a 3D perception model of the fire and could also be used for visualizing the fire evolution in remote computer systems. The presented system integrates the processing of images from visual and infrared cameras. It applies sensor fusion techniques involving also telemetry sensors, and GPS. The paper also includes some results of forest fire experiments.European Commission EVG1-CT-2001-00043European Commission IST-2001-34304Ministerio de Educación y Ciencia DPI2005-0229
Fast unsupervised multiresolution color image segmentation using adaptive gradient thresholding and progressive region growing
In this thesis, we propose a fast unsupervised multiresolution color image segmentation algorithm which takes advantage of gradient information in an adaptive and progressive framework. This gradient-based segmentation method is initialized by a vector gradient calculation on the full resolution input image in the CIE L*a*b* color space. The resultant edge map is used to adaptively generate thresholds for classifying regions of varying gradient densities at different levels of the input image pyramid, obtained through a dyadic wavelet decomposition scheme. At each level, the classification obtained by a progressively thresholded growth procedure is combined with an entropy-based texture model in a statistical merging procedure to obtain an interim segmentation. Utilizing an association of a gradient quantized confidence map and non-linear spatial filtering techniques, regions of high confidence are passed from one level to another until the full resolution segmentation is achieved. Evaluation of our results on several hundred images using the Normalized Probabilistic Rand (NPR) Index shows that our algorithm outperforms state-of the art segmentation techniques and is much more computationally efficient than its single scale counterpart, with comparable segmentation quality
Wavelets and their use
This review paper is intended to give a useful guide for those who want to
apply discrete wavelets in their practice. The notion of wavelets and their use
in practical computing and various applications are briefly described, but
rigorous proofs of mathematical statements are omitted, and the reader is just
referred to corresponding literature. The multiresolution analysis and fast
wavelet transform became a standard procedure for dealing with discrete
wavelets. The proper choice of a wavelet and use of nonstandard matrix
multiplication are often crucial for achievement of a goal. Analysis of various
functions with the help of wavelets allows to reveal fractal structures,
singularities etc. Wavelet transform of operator expressions helps solve some
equations. In practical applications one deals often with the discretized
functions, and the problem of stability of wavelet transform and corresponding
numerical algorithms becomes important. After discussing all these topics we
turn to practical applications of the wavelet machinery. They are so numerous
that we have to limit ourselves by some examples only. The authors would be
grateful for any comments which improve this review paper and move us closer to
the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh
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