13,877 research outputs found
Sparse Recovery from Combined Fusion Frame Measurements
Sparse representations have emerged as a powerful tool in signal and
information processing, culminated by the success of new acquisition and
processing techniques such as Compressed Sensing (CS). Fusion frames are very
rich new signal representation methods that use collections of subspaces
instead of vectors to represent signals. This work combines these exciting
fields to introduce a new sparsity model for fusion frames. Signals that are
sparse under the new model can be compressively sampled and uniquely
reconstructed in ways similar to sparse signals using standard CS. The
combination provides a promising new set of mathematical tools and signal
models useful in a variety of applications. With the new model, a sparse signal
has energy in very few of the subspaces of the fusion frame, although it does
not need to be sparse within each of the subspaces it occupies. This sparsity
model is captured using a mixed l1/l2 norm for fusion frames.
A signal sparse in a fusion frame can be sampled using very few random
projections and exactly reconstructed using a convex optimization that
minimizes this mixed l1/l2 norm. The provided sampling conditions generalize
coherence and RIP conditions used in standard CS theory. It is demonstrated
that they are sufficient to guarantee sparse recovery of any signal sparse in
our model. Moreover, a probabilistic analysis is provided using a stochastic
model on the sparse signal that shows that under very mild conditions the
probability of recovery failure decays exponentially with increasing dimension
of the subspaces
Graded quantization for multiple description coding of compressive measurements
Compressed sensing (CS) is an emerging paradigm for acquisition of compressed
representations of a sparse signal. Its low complexity is appealing for
resource-constrained scenarios like sensor networks. However, such scenarios
are often coupled with unreliable communication channels and providing robust
transmission of the acquired data to a receiver is an issue. Multiple
description coding (MDC) effectively combats channel losses for systems without
feedback, thus raising the interest in developing MDC methods explicitly
designed for the CS framework, and exploiting its properties. We propose a
method called Graded Quantization (CS-GQ) that leverages the democratic
property of compressive measurements to effectively implement MDC, and we
provide methods to optimize its performance. A novel decoding algorithm based
on the alternating directions method of multipliers is derived to reconstruct
signals from a limited number of received descriptions. Simulations are
performed to assess the performance of CS-GQ against other methods in presence
of packet losses. The proposed method is successful at providing robust coding
of CS measurements and outperforms other schemes for the considered test
metrics
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
Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors
The Kaczmarz algorithm is popular for iteratively solving an overdetermined
system of linear equations. The traditional Kaczmarz algorithm can approximate
the solution in few sweeps through the equations but a randomized version of
the Kaczmarz algorithm was shown to converge exponentially and independent of
number of equations. Recently an algorithm for finding sparse solution to a
linear system of equations has been proposed based on weighted randomized
Kaczmarz algorithm. These algorithms solves single measurement vector problem;
however there are applications were multiple-measurements are available. In
this work, the objective is to solve a multiple measurement vector problem with
common sparse support by modifying the randomized Kaczmarz algorithm. We have
also modeled the problem of face recognition from video as the multiple
measurement vector problem and solved using our proposed technique. We have
compared the proposed algorithm with state-of-art spectral projected gradient
algorithm for multiple measurement vectors on both real and synthetic datasets.
The Monte Carlo simulations confirms that our proposed algorithm have better
recovery and convergence rate than the MMV version of spectral projected
gradient algorithm under fairness constraints
SurfelWarp: Efficient Non-Volumetric Single View Dynamic Reconstruction
We contribute a dense SLAM system that takes a live stream of depth images as
input and reconstructs non-rigid deforming scenes in real time, without
templates or prior models. In contrast to existing approaches, we do not
maintain any volumetric data structures, such as truncated signed distance
function (TSDF) fields or deformation fields, which are performance and memory
intensive. Our system works with a flat point (surfel) based representation of
geometry, which can be directly acquired from commodity depth sensors. Standard
graphics pipelines and general purpose GPU (GPGPU) computing are leveraged for
all central operations: i.e., nearest neighbor maintenance, non-rigid
deformation field estimation and fusion of depth measurements. Our pipeline
inherently avoids expensive volumetric operations such as marching cubes,
volumetric fusion and dense deformation field update, leading to significantly
improved performance. Furthermore, the explicit and flexible surfel based
geometry representation enables efficient tackling of topology changes and
tracking failures, which makes our reconstructions consistent with updated
depth observations. Our system allows robots to maintain a scene description
with non-rigidly deformed objects that potentially enables interactions with
dynamic working environments.Comment: RSS 2018. The video and source code are available on
https://sites.google.com/view/surfelwarp/hom
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