33,481 research outputs found
Sparse Estimation with the Swept Approximated Message-Passing Algorithm
Approximate Message Passing (AMP) has been shown to be a superior method for
inference problems, such as the recovery of signals from sets of noisy,
lower-dimensionality measurements, both in terms of reconstruction accuracy and
in computational efficiency. However, AMP suffers from serious convergence
issues in contexts that do not exactly match its assumptions. We propose a new
approach to stabilizing AMP in these contexts by applying AMP updates to
individual coefficients rather than in parallel. Our results show that this
change to the AMP iteration can provide theoretically expected, but hitherto
unobtainable, performance for problems on which the standard AMP iteration
diverges. Additionally, we find that the computational costs of this swept
coefficient update scheme is not unduly burdensome, allowing it to be applied
efficiently to signals of large dimensionality.Comment: 11 pages, 3 figures, implementation available at
https://github.com/eric-tramel/SwAMP-Dem
Adaptive sensing performance lower bounds for sparse signal detection and support estimation
This paper gives a precise characterization of the fundamental limits of
adaptive sensing for diverse estimation and testing problems concerning sparse
signals. We consider in particular the setting introduced in (IEEE Trans.
Inform. Theory 57 (2011) 6222-6235) and show necessary conditions on the
minimum signal magnitude for both detection and estimation: if is a sparse vector with non-zero components then it
can be reliably detected in noise provided the magnitude of the non-zero
components exceeds . Furthermore, the signal support can be exactly
identified provided the minimum magnitude exceeds . Notably
there is no dependence on , the extrinsic signal dimension. These results
show that the adaptive sensing methodologies proposed previously in the
literature are essentially optimal, and cannot be substantially improved. In
addition, these results provide further insights on the limits of adaptive
compressive sensing.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ555 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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
Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation
Adaptive sampling results in dramatic improvements in the recovery of sparse
signals in white Gaussian noise. A sequential adaptive sampling-and-refinement
procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form
of multi-stage experimental design and testing. Because of the adaptive nature
of the data collection, DS can detect and localize far weaker signals than
possible from non-adaptive measurements. In particular, reliable detection and
localization (support estimation) using non-adaptive samples is possible only
if the signal amplitudes grow logarithmically with the problem dimension. Here
it is shown that using adaptive sampling, reliable detection is possible
provided the amplitude exceeds a constant, and localization is possible when
the amplitude exceeds any arbitrarily slowly growing function of the dimension.Comment: 23 pages, 2 figures. Revision includes minor clarifications, along
with more illustrative experimental results (cf. Figure 2
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