7,777 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
Compressed sensing in astronomy and remote sensing: a data fusion perspective
Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that provides an alternative to the well-known Shannon sampling theory. In this paper we investigate how compressed sensing (CS) can provide new insights into astronomical data compression. In a previous study1 we gave new insights into the use of Compressed Sensing (CS) in the scope of astronomical data analysis. More specifically, we showed how CS is flexible enough to account for particular observational strategies such as raster scans. This kind of CS data fusion concept led to an elegant and effective way to solve the problem ESA is faced with, for the transmission to the earth of the data collected by PACS, one of the instruments onboard the Herschel spacecraft which will launched in late 2008/early 2009. In this paper, we extend this work by showing how CS can be effectively used to jointly decode multiple observations at the level of map making. This allows us to directly estimate large areas of the sky from one or several raster scans. Beyond the particular but important Herschel example, we strongly believe that CS can be applied to a wider range of applications such as in earth science and remote sensing where dealing with multiple redundant observations is common place. Simple but illustrative examples are given that show the effectiveness of CS when decoding is made from multiple redundant observations
Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications
Modern scientific instruments produce vast amounts of data, which can
overwhelm the processing ability of computer systems. Lossy compression of data
is an intriguing solution, but comes with its own drawbacks, such as potential
signal loss, and the need for careful optimization of the compression ratio. In
this work, we focus on a setting where this problem is especially acute:
compressive sensing frameworks for interferometry and medical imaging. We ask
the following question: can the precision of the data representation be lowered
for all inputs, with recovery guarantees and practical performance? Our first
contribution is a theoretical analysis of the normalized Iterative Hard
Thresholding (IHT) algorithm when all input data, meaning both the measurement
matrix and the observation vector are quantized aggressively. We present a
variant of low precision normalized {IHT} that, under mild conditions, can
still provide recovery guarantees. The second contribution is the application
of our quantization framework to radio astronomy and magnetic resonance
imaging. We show that lowering the precision of the data can significantly
accelerate image recovery. We evaluate our approach on telescope data and
samples of brain images using CPU and FPGA implementations achieving up to a 9x
speed-up with negligible loss of recovery quality.Comment: 19 pages, 5 figures, 1 table, in IEEE Transactions on Signal
Processin
Compressed sensing imaging techniques for radio interferometry
Radio interferometry probes astrophysical signals through incomplete and
noisy Fourier measurements. The theory of compressed sensing demonstrates that
such measurements may actually suffice for accurate reconstruction of sparse or
compressible signals. We propose new generic imaging techniques based on convex
optimization for global minimization problems defined in this context. The
versatility of the framework notably allows introduction of specific prior
information on the signals, which offers the possibility of significant
improvements of reconstruction relative to the standard local matching pursuit
algorithm CLEAN used in radio astronomy. We illustrate the potential of the
approach by studying reconstruction performances on simulations of two
different kinds of signals observed with very generic interferometric
configurations. The first kind is an intensity field of compact astrophysical
objects. The second kind is the imprint of cosmic strings in the temperature
field of the cosmic microwave background radiation, of particular interest for
cosmology.Comment: 10 pages, 1 figure. Version 2 matches version accepted for
publication in MNRAS. Changes includes: writing corrections, clarifications
of arguments, figure update, and a new subsection 4.1 commenting on the exact
compliance of radio interferometric measurements with compressed sensin
Solar hard X-ray imaging by means of Compressed Sensing and Finite Isotropic Wavelet Transform
This paper shows that compressed sensing realized by means of regularized
deconvolution and the Finite Isotropic Wavelet Transform is effective and
reliable in hard X-ray solar imaging.
The method utilizes the Finite Isotropic Wavelet Transform with Meyer
function as the mother wavelet. Further, compressed sensing is realized by
optimizing a sparsity-promoting regularized objective function by means of the
Fast Iterative Shrinkage-Thresholding Algorithm. Eventually, the regularization
parameter is selected by means of the Miller criterion.
The method is applied against both synthetic data mimicking the
Spectrometer/Telescope Imaging X-rays (STIX) measurements and experimental
observations provided by the Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI). The performances of the method are compared with the results
provided by standard visibility-based reconstruction methods.
The results show that the application of the sparsity constraint and the use
of a continuous, isotropic framework for the wavelet transform provide a
notable spatial accuracy and significantly reduce the ringing effects due to
the instrument point spread functions
Compressed Sensing - A New mode of Measurement
After introducing the concept of compressed sensing as a complementary
measurement mode to the classical Shannon-Nyquist approach, I discuss some of
the drivers, potential challenges and obstacles to its implementation. I end with a
speculative attempt to embed compressed sensing as an enabling methodology
within the emergence of data-driven discovery. As a consequence I predict the
growth of non-nomological sciences where heuristic correlations will find
applications but often bypass conventional pure basic and use-inspired basic
research stages due to the lack of verifiable hypotheses
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