3,211 research outputs found
Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation
We study the compressed sensing (CS) signal estimation problem where an input
signal is measured via a linear matrix multiplication under additive noise.
While this setup usually assumes sparsity or compressibility in the input
signal during recovery, the signal structure that can be leveraged is often not
known a priori. In this paper, we consider universal CS recovery, where the
statistics of a stationary ergodic signal source are estimated simultaneously
with the signal itself. Inspired by Kolmogorov complexity and minimum
description length, we focus on a maximum a posteriori (MAP) estimation
framework that leverages universal priors to match the complexity of the
source. Our framework can also be applied to general linear inverse problems
where more measurements than in CS might be needed. We provide theoretical
results that support the algorithmic feasibility of universal MAP estimation
using a Markov chain Monte Carlo implementation, which is computationally
challenging. We incorporate some techniques to accelerate the algorithm while
providing comparable and in many cases better reconstruction quality than
existing algorithms. Experimental results show the promise of universality in
CS, particularly for low-complexity sources that do not exhibit standard
sparsity or compressibility.Comment: 29 pages, 8 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
Adaptive-Rate Compressive Sensing Using Side Information
We provide two novel adaptive-rate compressive sensing (CS) strategies for
sparse, time-varying signals using side information. Our first method utilizes
extra cross-validation measurements, and the second one exploits extra
low-resolution measurements. Unlike the majority of current CS techniques, we
do not assume that we know an upper bound on the number of significant
coefficients that comprise the images in the video sequence. Instead, we use
the side information to predict the number of significant coefficients in the
signal at the next time instant. For each image in the video sequence, our
techniques specify a fixed number of spatially-multiplexed CS measurements to
acquire, and adjust this quantity from image to image. Our strategies are
developed in the specific context of background subtraction for surveillance
video, and we experimentally validate the proposed methods on real video
sequences
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