20,336 research outputs found
Unveiling The Tree: A Convex Framework for Sparse Problems
This paper presents a general framework for generating greedy algorithms for
solving convex constraint satisfaction problems for sparse solutions by mapping
the satisfaction problem into one of graph traversal on a rooted tree of
unknown topology. For every pre-walk of the tree an initial set of generally
dense feasible solutions is processed in such a way that the sparsity of each
solution increases with each generation unveiled. The specific computation
performed at any particular child node is shown to correspond to an embedding
of a polytope into the polytope received from that nodes parent. Several issues
related to pre-walk order selection, computational complexity and tractability,
and the use of heuristic and/or side information is discussed. An example of a
single-path, depth-first algorithm on a tree with randomized vertex reduction
and a run-time path selection algorithm is presented in the context of sparse
lowpass filter design
Quick and energy-efficient Bayesian computing of binocular disparity using stochastic digital signals
Reconstruction of the tridimensional geometry of a visual scene using the
binocular disparity information is an important issue in computer vision and
mobile robotics, which can be formulated as a Bayesian inference problem.
However, computation of the full disparity distribution with an advanced
Bayesian model is usually an intractable problem, and proves computationally
challenging even with a simple model. In this paper, we show how probabilistic
hardware using distributed memory and alternate representation of data as
stochastic bitstreams can solve that problem with high performance and energy
efficiency. We put forward a way to express discrete probability distributions
using stochastic data representations and perform Bayesian fusion using those
representations, and show how that approach can be applied to diparity
computation. We evaluate the system using a simulated stochastic implementation
and discuss possible hardware implementations of such architectures and their
potential for sensorimotor processing and robotics.Comment: Preprint of article submitted for publication in International
Journal of Approximate Reasoning and accepted pending minor revision
Convexity in source separation: Models, geometry, and algorithms
Source separation or demixing is the process of extracting multiple
components entangled within a signal. Contemporary signal processing presents a
host of difficult source separation problems, from interference cancellation to
background subtraction, blind deconvolution, and even dictionary learning.
Despite the recent progress in each of these applications, advances in
high-throughput sensor technology place demixing algorithms under pressure to
accommodate extremely high-dimensional signals, separate an ever larger number
of sources, and cope with more sophisticated signal and mixing models. These
difficulties are exacerbated by the need for real-time action in automated
decision-making systems.
Recent advances in convex optimization provide a simple framework for
efficiently solving numerous difficult demixing problems. This article provides
an overview of the emerging field, explains the theory that governs the
underlying procedures, and surveys algorithms that solve them efficiently. We
aim to equip practitioners with a toolkit for constructing their own demixing
algorithms that work, as well as concrete intuition for why they work
Physical Layer Service Integration in 5G: Potentials and Challenges
High transmission rate and secure communication have been identified as the
key targets that need to be effectively addressed by fifth generation (5G)
wireless systems. In this context, the concept of physical-layer security
becomes attractive, as it can establish perfect security using only the
characteristics of wireless medium. Nonetheless, to further increase the
spectral efficiency, an emerging concept, termed physical-layer service
integration (PHY-SI), has been recognized as an effective means. Its basic idea
is to combine multiple coexisting services, i.e., multicast/broadcast service
and confidential service, into one integral service for one-time transmission
at the transmitter side. This article first provides a tutorial on typical
PHY-SI models. Furthermore, we propose some state-of-the-art solutions to
improve the overall performance of PHY-SI in certain important communication
scenarios. In particular, we highlight the extension of several concepts
borrowed from conventional single-service communications, such as artificial
noise (AN), eigenmode transmission etc., to the scenario of PHY-SI. These
techniques are shown to be effective in the design of reliable and robust
PHY-SI schemes. Finally, several potential research directions are identified
for future work.Comment: 12 pages, 7 figure
Metropolis Sampling
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference,
system simulation and optimization problems. The Markov Chain Monte Carlo
(MCMC) algorithms are a well-known class of MC methods which generate a Markov
chain with the desired invariant distribution. In this document, we focus on
the Metropolis-Hastings (MH) sampler, which can be considered as the atom of
the MCMC techniques, introducing the basic notions and different properties. We
describe in details all the elements involved in the MH algorithm and the most
relevant variants. Several improvements and recent extensions proposed in the
literature are also briefly discussed, providing a quick but exhaustive
overview of the current Metropolis-based sampling's world.Comment: Wiley StatsRef-Statistics Reference Online, 201
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