2,930 research outputs found
Information-Theoretic Compressive Measurement Design
An information-theoretic projection design framework is proposed, of interest for feature design and compressive measurements. Both Gaussian and Poisson measurement models are considered. The gradient of a proposed information-theoretic metric (ITM) is derived, and a gradient-descent algorithm is applied in design; connections are made to the information bottleneck. The fundamental solution structure of such design is revealed in the case of a Gaussian measurement model and arbitrary input statistics. This new theoretical result reveals how ITM parameter settings impact the number of needed projection measurements, with this verified experimentally. The ITM achieves promising results on real data, for both signal recovery and classification
Info-Greedy sequential adaptive compressed sensing
We present an information-theoretic framework for sequential adaptive
compressed sensing, Info-Greedy Sensing, where measurements are chosen to
maximize the extracted information conditioned on the previous measurements. We
show that the widely used bisection approach is Info-Greedy for a family of
-sparse signals by connecting compressed sensing and blackbox complexity of
sequential query algorithms, and present Info-Greedy algorithms for Gaussian
and Gaussian Mixture Model (GMM) signals, as well as ways to design sparse
Info-Greedy measurements. Numerical examples demonstrate the good performance
of the proposed algorithms using simulated and real data: Info-Greedy Sensing
shows significant improvement over random projection for signals with sparse
and low-rank covariance matrices, and adaptivity brings robustness when there
is a mismatch between the assumed and the true distributions.Comment: Preliminary results presented at Allerton Conference 2014. To appear
in IEEE Journal Selected Topics on Signal Processin
Compressive Measurement Designs for Estimating Structured Signals in Structured Clutter: A Bayesian Experimental Design Approach
This work considers an estimation task in compressive sensing, where the goal
is to estimate an unknown signal from compressive measurements that are
corrupted by additive pre-measurement noise (interference, or clutter) as well
as post-measurement noise, in the specific setting where some (perhaps limited)
prior knowledge on the signal, interference, and noise is available. The
specific aim here is to devise a strategy for incorporating this prior
information into the design of an appropriate compressive measurement strategy.
Here, the prior information is interpreted as statistics of a prior
distribution on the relevant quantities, and an approach based on Bayesian
Experimental Design is proposed. Experimental results on synthetic data
demonstrate that the proposed approach outperforms traditional random
compressive measurement designs, which are agnostic to the prior information,
as well as several other knowledge-enhanced sensing matrix designs based on
more heuristic notions.Comment: 5 pages, 4 figures. Accepted for publication at The Asilomar
Conference on Signals, Systems, and Computers 201
Compressed sensing using sparse binary measurements: a rateless coding perspective
Compressed Sensing (CS) methods using sparse binary measurement matrices and iterative message-passing re- covery procedures have been recently investigated due to their low computational complexity and excellent performance. Drawing much of inspiration from sparse-graph codes such as Low-Density Parity-Check (LDPC) codes, these studies use analytical tools from modern coding theory to analyze CS solutions. In this paper, we consider and systematically analyze the CS setup inspired by a class of efficient, popular and flexible sparse-graph codes called rateless codes. The proposed rateless CS setup is asymptotically analyzed using tools such as Density Evolution and EXIT charts and fine-tuned using degree distribution optimization techniques
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