1,813 research outputs found
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
How to find real-world applications for compressive sensing
The potential of compressive sensing (CS) has spurred great interest in the
research community and is a fast growing area of research. However, research
translating CS theory into practical hardware and demonstrating clear and
significant benefits with this hardware over current, conventional imaging
techniques has been limited. This article helps researchers to find those niche
applications where the CS approach provides substantial gain over conventional
approaches by articulating lessons learned in finding one such application; sea
skimming missile detection. As a proof of concept, it is demonstrated that a
simplified CS missile detection architecture and algorithm provides comparable
results to the conventional imaging approach but using a smaller FPA. The
primary message is that all of the excitement surrounding CS is necessary and
appropriate for encouraging our creativity but we all must also take off our
"rose colored glasses" and critically judge our ideas, methods and results
relative to conventional imaging approaches.Comment: 10 page
The application of compressive sampling to radio astronomy I: Deconvolution
Compressive sampling is a new paradigm for sampling, based on sparseness of
signals or signal representations. It is much less restrictive than
Nyquist-Shannon sampling theory and thus explains and systematises the
widespread experience that methods such as the H\"ogbom CLEAN can violate the
Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution
method for extended sources is introduced. This method can reconstruct both
point sources and extended sources (using the isotropic undecimated wavelet
transform as a basis function for the reconstruction step). We compare this
CS-based deconvolution method with two CLEAN-based deconvolution methods: the
H\"ogbom CLEAN and the multiscale CLEAN. This new method shows the best
performance in deconvolving extended sources for both uniform and natural
weighting of the sampled visibilities. Both visual and numerical results of the
comparison are provided.Comment: Published by A&A, Matlab code can be found:
http://code.google.com/p/csra/download
On sparsity averaging
Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013)
introduced a novel regularization method for compressive imaging in the context
of compressed sensing with coherent redundant dictionaries. The approach relies
on the observation that natural images exhibit strong average sparsity over
multiple coherent frames. The associated reconstruction algorithm, based on an
analysis prior and a reweighted scheme, is dubbed Sparsity Averaging
Reweighted Analysis (SARA). We review these advances and extend associated
simulations establishing the superiority of SARA to regularization methods
based on sparsity in a single frame, for a generic spread spectrum acquisition
and for a Fourier acquisition of particular interest in radio astronomy.Comment: 4 pages, 3 figures, Proceedings of 10th International Conference on
Sampling Theory and Applications (SampTA), Code available at
https://github.com/basp-group/sopt, Full journal letter available at
http://arxiv.org/abs/arXiv:1208.233
Robust sparse image reconstruction of radio interferometric observations with purify
Next-generation radio interferometers, such as the Square Kilometre Array
(SKA), will revolutionise our understanding of the universe through their
unprecedented sensitivity and resolution. However, to realise these goals
significant challenges in image and data processing need to be overcome. The
standard methods in radio interferometry for reconstructing images, such as
CLEAN, have served the community well over the last few decades and have
survived largely because they are pragmatic. However, they produce
reconstructed inter\-ferometric images that are limited in quality and
scalability for big data. In this work we apply and evaluate alternative
interferometric reconstruction methods that make use of state-of-the-art sparse
image reconstruction algorithms motivated by compressive sensing, which have
been implemented in the PURIFY software package. In particular, we implement
and apply the proximal alternating direction method of multipliers (P-ADMM)
algorithm presented in a recent article. First, we assess the impact of the
interpolation kernel used to perform gridding and degridding on sparse image
reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as
well as prolate spheroidal wave functions, while providing a computational
saving and an analytic form. Second, we apply PURIFY to real interferometric
observations from the Very Large Array (VLA) and the Australia Telescope
Compact Array (ATCA) and find images recovered by PURIFY are higher quality
than those recovered by CLEAN. Third, we discuss how PURIFY reconstructions
exhibit additional advantages over those recovered by CLEAN. The latest version
of PURIFY, with developments presented in this work, is made publicly
available.Comment: 22 pages, 10 figures, PURIFY code available at
http://basp-group.github.io/purif
Compressive Wavefront Sensing with Weak Values
We demonstrate a wavefront sensor based on the compressive sensing,
single-pixel camera. Using a high-resolution spatial light modulator (SLM) as a
variable waveplate, we weakly couple an optical field's transverse-position and
polarization degrees of freedom. By placing random, binary patterns on the SLM,
polarization serves as a meter for directly measuring random projections of the
real and imaginary components of the wavefront. Compressive sensing techniques
can then recover the wavefront. We acquire high quality, 256x256 pixel images
of the wavefront from only 10,000 projections. Photon-counting detectors give
sub-picowatt sensitivity
PURIFY: a new algorithmic framework for next-generation radio-interferometric imaging
In recent works, compressed sensing (CS) and convex opti- mization techniques have been applied to radio-interferometric imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. We review our latest contributions [1, 2, 3], which leverage the versatility of convex optimization to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted in a new software PURIFY (beta version) relies on the simultaneous-direction method of multipliers (SDMM). The performance of various sparsity priors is evaluated through simulations in the continuous visibility setting, confirming the superiority of our recent average sparsity approach SARA
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