541 research outputs found
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
Sequential Sensing with Model Mismatch
We characterize the performance of sequential information guided sensing,
Info-Greedy Sensing, when there is a mismatch between the true signal model and
the assumed model, which may be a sample estimate. In particular, we consider a
setup where the signal is low-rank Gaussian and the measurements are taken in
the directions of eigenvectors of the covariance matrix in a decreasing order
of eigenvalues. We establish a set of performance bounds when a mismatched
covariance matrix is used, in terms of the gap of signal posterior entropy, as
well as the additional amount of power required to achieve the same signal
recovery precision. Based on this, we further study how to choose an
initialization for Info-Greedy Sensing using the sample covariance matrix, or
using an efficient covariance sketching scheme.Comment: Submitted to IEEE for publicatio
Adaptive Non-uniform Compressive Sampling for Time-varying Signals
In this paper, adaptive non-uniform compressive sampling (ANCS) of
time-varying signals, which are sparse in a proper basis, is introduced. ANCS
employs the measurements of previous time steps to distribute the sensing
energy among coefficients more intelligently. To this aim, a Bayesian inference
method is proposed that does not require any prior knowledge of importance
levels of coefficients or sparsity of the signal. Our numerical simulations
show that ANCS is able to achieve the desired non-uniform recovery of the
signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce
the number of required measurements significantly.Comment: 6 pages, 8 figures, Conference on Information Sciences and Systems
(CISS 2017) Baltimore, Marylan
Sparse Representation of Astronomical Images
Sparse representation of astronomical images is discussed. It is shown that a
significant gain in sparsity is achieved when particular mixed dictionaries are
used for approximating these types of images with greedy selection strategies.
Experiments are conducted to confirm: i)Effectiveness at producing sparse
representations. ii)Competitiveness, with respect to the time required to
process large images.The latter is a consequence of the suitability of the
proposed dictionaries for approximating images in partitions of small
blocks.This feature makes it possible to apply the effective greedy selection
technique Orthogonal Matching Pursuit, up to some block size. For blocks
exceeding that size a refinement of the original Matching Pursuit approach is
considered. The resulting method is termed Self Projected Matching Pursuit,
because is shown to be effective for implementing, via Matching Pursuit itself,
the optional back-projection intermediate steps in that approach.Comment: Software to implement the approach is available on
http://www.nonlinear-approx.info/examples/node1.htm
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