2,881 research outputs found
Distributed soft thresholding for sparse signal recovery
In this paper, we address the problem of distributed sparse recovery of
signals acquired via compressed measurements in a sensor network. We propose a
new class of distributed algorithms to solve Lasso regression problems, when
the communication to a fusion center is not possible, e.g., due to
communication cost or privacy reasons. More precisely, we introduce a
distributed iterative soft thresholding algorithm (DISTA) that consists of
three steps: an averaging step, a gradient step, and a soft thresholding
operation. We prove the convergence of DISTA in networks represented by regular
graphs, and we compare it with existing methods in terms of performance,
memory, and complexity.Comment: Revised version. Main improvements: extension of the convergence
theorem to regular graphs; new numerical results and comparisons with other
algorithm
Sparse Solution of Underdetermined Linear Equations via Adaptively Iterative Thresholding
Finding the sparset solution of an underdetermined system of linear equations
has attracted considerable attention in recent years. Among a large
number of algorithms, iterative thresholding algorithms are recognized as one
of the most efficient and important classes of algorithms. This is mainly due
to their low computational complexities, especially for large scale
applications. The aim of this paper is to provide guarantees on the global
convergence of a wide class of iterative thresholding algorithms. Since the
thresholds of the considered algorithms are set adaptively at each iteration,
we call them adaptively iterative thresholding (AIT) algorithms. As the main
result, we show that as long as satisfies a certain coherence property, AIT
algorithms can find the correct support set within finite iterations, and then
converge to the original sparse solution exponentially fast once the correct
support set has been identified. Meanwhile, we also demonstrate that AIT
algorithms are robust to the algorithmic parameters. In addition, it should be
pointed out that most of the existing iterative thresholding algorithms such as
hard, soft, half and smoothly clipped absolute deviation (SCAD) algorithms are
included in the class of AIT algorithms studied in this paper.Comment: 33 pages, 1 figur
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
Maximin Analysis of Message Passing Algorithms for Recovering Block Sparse Signals
We consider the problem of recovering a block (or group) sparse signal from
an underdetermined set of random linear measurements, which appear in
compressed sensing applications such as radar and imaging. Recent results of
Donoho, Johnstone, and Montanari have shown that approximate message passing
(AMP) in combination with Stein's shrinkage outperforms group LASSO for large
block sizes. In this paper, we prove that, for a fixed block size and in the
strong undersampling regime (i.e., having very few measurements compared to the
ambient dimension), AMP cannot improve upon group LASSO, thereby complementing
the results of Donoho et al
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