2,554 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
GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring
Compressive sensing promises to enable bandwidth-efficient on-board
compression of astronomical data by lifting the encoding complexity from the
source to the receiver. The signal is recovered off-line, exploiting GPUs
parallel computation capabilities to speedup the reconstruction process.
However, inherent GPU hardware constraints limit the size of the recoverable
signal and the speedup practically achievable. In this work, we design parallel
algorithms that exploit the properties of circulant matrices for efficient
GPU-accelerated sparse signals recovery. Our approach reduces the memory
requirements, allowing us to recover very large signals with limited memory. In
addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc
parallelization of matrix-vector multiplications and matrix inversions.
Finally, we practically demonstrate our algorithms in a typical application of
circulant matrices: deblurring a sparse astronomical image in the compressed
domain
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
Superresolution without Separation
This paper provides a theoretical analysis of diffraction-limited
superresolution, demonstrating that arbitrarily close point sources can be
resolved in ideal situations. Precisely, we assume that the incoming signal is
a linear combination of M shifted copies of a known waveform with unknown
shifts and amplitudes, and one only observes a finite collection of evaluations
of this signal. We characterize properties of the base waveform such that the
exact translations and amplitudes can be recovered from 2M + 1 observations.
This recovery is achieved by solving a a weighted version of basis pursuit over
a continuous dictionary. Our methods combine classical polynomial interpolation
techniques with contemporary tools from compressed sensing.Comment: 23 pages, 8 figure
LOFAR Sparse Image Reconstruction
Context. The LOw Frequency ARray (LOFAR) radio telescope is a giant digital
phased array interferometer with multiple antennas distributed in Europe. It
provides discrete sets of Fourier components of the sky brightness. Recovering
the original brightness distribution with aperture synthesis forms an inverse
problem that can be solved by various deconvolution and minimization methods
Aims. Recent papers have established a clear link between the discrete nature
of radio interferometry measurement and the "compressed sensing" (CS) theory,
which supports sparse reconstruction methods to form an image from the measured
visibilities. Empowered by proximal theory, CS offers a sound framework for
efficient global minimization and sparse data representation using fast
algorithms. Combined with instrumental direction-dependent effects (DDE) in the
scope of a real instrument, we developed and validated a new method based on
this framework Methods. We implemented a sparse reconstruction method in the
standard LOFAR imaging tool and compared the photometric and resolution
performance of this new imager with that of CLEAN-based methods (CLEAN and
MS-CLEAN) with simulated and real LOFAR data Results. We show that i) sparse
reconstruction performs as well as CLEAN in recovering the flux of point
sources; ii) performs much better on extended objects (the root mean square
error is reduced by a factor of up to 10); and iii) provides a solution with an
effective angular resolution 2-3 times better than the CLEAN images.
Conclusions. Sparse recovery gives a correct photometry on high dynamic and
wide-field images and improved realistic structures of extended sources (of
simulated and real LOFAR datasets). This sparse reconstruction method is
compatible with modern interferometric imagers that handle DDE corrections (A-
and W-projections) required for current and future instruments such as LOFAR
and SKAComment: Published in A&A, 19 pages, 9 figure
Green compressive sampling reconstruction in IoT networks
In this paper, we address the problem of green Compressed Sensing (CS) reconstruction within Internet of Things (IoT) networks, both in terms of computing architecture and reconstruction algorithms. The approach is novel since, unlike most of the literature dealing with energy efficient gathering of the CS measurements, we focus on the energy efficiency of the signal reconstruction stage given the CS measurements. As a first novel contribution, we present an analysis of the energy consumption within the IoT network under two computing architectures. In the first one, reconstruction takes place within the IoT network and the reconstructed data are encoded and transmitted out of the IoT network; in the second one, all the CS measurements are forwarded to off-network devices for reconstruction and storage, i.e., reconstruction is off-loaded. Our analysis shows that the two architectures significantly differ in terms of consumed energy, and it outlines a theoretically motivated criterion to select a green CS reconstruction computing architecture. Specifically, we present a suitable decision function to determine which architecture outperforms the other in terms of energy efficiency. The presented decision function depends on a few IoT network features, such as the network size, the sink connectivity, and other systems’ parameters. As a second novel contribution, we show how to overcome classical performance comparison of different CS reconstruction algorithms usually carried out w.r.t. the achieved accuracy. Specifically, we consider the consumed energy and analyze the energy vs. accuracy trade-off. The herein presented approach, jointly considering signal processing and IoT network issues, is a relevant contribution for designing green compressive sampling architectures in IoT networks
Sampling and Recovery of Pulse Streams
Compressive Sensing (CS) is a new technique for the efficient acquisition of
signals, images, and other data that have a sparse representation in some
basis, frame, or dictionary. By sparse we mean that the N-dimensional basis
representation has just K<<N significant coefficients; in this case, the CS
theory maintains that just M = K log N random linear signal measurements will
both preserve all of the signal information and enable robust signal
reconstruction in polynomial time. In this paper, we extend the CS theory to
pulse stream data, which correspond to S-sparse signals/images that are
convolved with an unknown F-sparse pulse shape. Ignoring their convolutional
structure, a pulse stream signal is K=SF sparse. Such signals figure
prominently in a number of applications, from neuroscience to astronomy. Our
specific contributions are threefold. First, we propose a pulse stream signal
model and show that it is equivalent to an infinite union of subspaces. Second,
we derive a lower bound on the number of measurements M required to preserve
the essential information present in pulse streams. The bound is linear in the
total number of degrees of freedom S + F, which is significantly smaller than
the naive bound based on the total signal sparsity K=SF. Third, we develop an
efficient signal recovery algorithm that infers both the shape of the impulse
response as well as the locations and amplitudes of the pulses. The algorithm
alternatively estimates the pulse locations and the pulse shape in a manner
reminiscent of classical deconvolution algorithms. Numerical experiments on
synthetic and real data demonstrate the advantages of our approach over
standard CS
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