38,939 research outputs found
Vector field reconstruction from sparse samples with applications
Abstract. We present a novel algorithm for 2D vector field reconstruction from sparse set of points–vectors pairs. Our approach subdivides the domain adaptively in order to make local piecewise polynomial approximations for the field. It uses partition of unity to blend those local approximations together, generating a global approximation for the field. The flexibility of this scheme allows handling data from very different sources. In particular, this work presents important applications of the proposed method to velocity and acceleration fields ’ analysis, in particular for fluid dynamics visualization
Pushing towards the Limit of Sampling Rate: Adaptive Chasing Sampling
Measurement samples are often taken in various monitoring applications. To
reduce the sensing cost, it is desirable to achieve better sensing quality
while using fewer samples. Compressive Sensing (CS) technique finds its role
when the signal to be sampled meets certain sparsity requirements. In this
paper we investigate the possibility and basic techniques that could further
reduce the number of samples involved in conventional CS theory by exploiting
learning-based non-uniform adaptive sampling.
Based on a typical signal sensing application, we illustrate and evaluate the
performance of two of our algorithms, Individual Chasing and Centroid Chasing,
for signals of different distribution features. Our proposed learning-based
adaptive sampling schemes complement existing efforts in CS fields and do not
depend on any specific signal reconstruction technique. Compared to
conventional sparse sampling methods, the simulation results demonstrate that
our algorithms allow less number of samples for accurate signal
reconstruction and achieve up to smaller signal reconstruction error
under the same noise condition.Comment: 9 pages, IEEE MASS 201
Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals
We demonstrate that the global fields of temperature, humidity and
geopotential heights admit a nearly sparse representation in the wavelet
domain, offering a viable path forward to explore new paradigms of
sparsity-promoting data assimilation and compressive recovery of land
surface-atmospheric states from space. We illustrate this idea using retrieval
products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave
Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the
sparsity of the fields of temperature is relatively pressure-independent while
atmospheric humidity and geopotential heights are typically sparser at lower
and higher pressure levels, respectively. We provide evidence that these
land-atmospheric states can be accurately estimated using a small set of
measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing
We demonstrate that sub-wavelength optical images borne on
partially-spatially-incoherent light can be recovered, from their far-field or
from the blurred image, given the prior knowledge that the image is sparse, and
only that. The reconstruction method relies on the recently demonstrated
sparsity-based sub-wavelength imaging. However, for
partially-spatially-incoherent light, the relation between the measurements and
the image is quadratic, yielding non-convex measurement equations that do not
conform to previously used techniques. Consequently, we demonstrate new
algorithmic methodology, referred to as quadratic compressed sensing, which can
be applied to a range of other problems involving information recovery from
partial correlation measurements, including when the correlation function has
local dependencies. Specifically for microscopy, this method can be readily
extended to white light microscopes with the additional knowledge of the light
source spectrum.Comment: 16 page
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
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