3,949 research outputs found
Compressed Sensing and Parallel Acquisition
Parallel acquisition systems arise in various applications in order to
moderate problems caused by insufficient measurements in single-sensor systems.
These systems allow simultaneous data acquisition in multiple sensors, thus
alleviating such problems by providing more overall measurements. In this work
we consider the combination of compressed sensing with parallel acquisition. We
establish the theoretical improvements of such systems by providing recovery
guarantees for which, subject to appropriate conditions, the number of
measurements required per sensor decreases linearly with the total number of
sensors. Throughout, we consider two different sampling scenarios -- distinct
(corresponding to independent sampling in each sensor) and identical
(corresponding to dependent sampling between sensors) -- and a general
mathematical framework that allows for a wide range of sensing matrices (e.g.,
subgaussian random matrices, subsampled isometries, random convolutions and
random Toeplitz matrices). We also consider not just the standard sparse signal
model, but also the so-called sparse in levels signal model. This model
includes both sparse and distributed signals and clustered sparse signals. As
our results show, optimal recovery guarantees for both distinct and identical
sampling are possible under much broader conditions on the so-called sensor
profile matrices (which characterize environmental conditions between a source
and the sensors) for the sparse in levels model than for the sparse model. To
verify our recovery guarantees we provide numerical results showing phase
transitions for a number of different multi-sensor environments.Comment: 43 pages, 4 figure
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
Structured random measurements in signal processing
Compressed sensing and its extensions have recently triggered interest in
randomized signal acquisition. A key finding is that random measurements
provide sparse signal reconstruction guarantees for efficient and stable
algorithms with a minimal number of samples. While this was first shown for
(unstructured) Gaussian random measurement matrices, applications require
certain structure of the measurements leading to structured random measurement
matrices. Near optimal recovery guarantees for such structured measurements
have been developed over the past years in a variety of contexts. This article
surveys the theory in three scenarios: compressed sensing (sparse recovery),
low rank matrix recovery, and phaseless estimation. The random measurement
matrices to be considered include random partial Fourier matrices, partial
random circulant matrices (subsampled convolutions), matrix completion, and
phase estimation from magnitudes of Fourier type measurements. The article
concludes with a brief discussion of the mathematical techniques for the
analysis of such structured random measurements.Comment: 22 pages, 2 figure
Compressively characterizing high-dimensional entangled states with complementary, random filtering
The resources needed to conventionally characterize a quantum system are
overwhelmingly large for high- dimensional systems. This obstacle may be
overcome by abandoning traditional cornerstones of quantum measurement, such as
general quantum states, strong projective measurement, and assumption-free
characterization. Following this reasoning, we demonstrate an efficient
technique for characterizing high-dimensional, spatial entanglement with one
set of measurements. We recover sharp distributions with local, random
filtering of the same ensemble in momentum followed by position---something the
uncertainty principle forbids for projective measurements. Exploiting the
expectation that entangled signals are highly correlated, we use fewer than
5,000 measurements to characterize a 65, 536-dimensional state. Finally, we use
entropic inequalities to witness entanglement without a density matrix. Our
method represents the sea change unfolding in quantum measurement where methods
influenced by the information theory and signal-processing communities replace
unscalable, brute-force techniques---a progression previously followed by
classical sensing.Comment: 13 pages, 7 figure
Toward Depth Estimation Using Mask-Based Lensless Cameras
Recently, coded masks have been used to demonstrate a thin form-factor
lensless camera, FlatCam, in which a mask is placed immediately on top of a
bare image sensor. In this paper, we present an imaging model and algorithm to
jointly estimate depth and intensity information in the scene from a single or
multiple FlatCams. We use a light field representation to model the mapping of
3D scene onto the sensor in which light rays from different depths yield
different modulation patterns. We present a greedy depth pursuit algorithm to
search the 3D volume and estimate the depth and intensity of each pixel within
the camera field-of-view. We present simulation results to analyze the
performance of our proposed model and algorithm with different FlatCam
settings
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