7,405 research outputs found
A Max-Product EM Algorithm for Reconstructing Markov-tree Sparse Signals from Compressive Samples
We propose a Bayesian expectation-maximization (EM) algorithm for
reconstructing Markov-tree sparse signals via belief propagation. The
measurements follow an underdetermined linear model where the
regression-coefficient vector is the sum of an unknown approximately sparse
signal and a zero-mean white Gaussian noise with an unknown variance. The
signal is composed of large- and small-magnitude components identified by
binary state variables whose probabilistic dependence structure is described by
a Markov tree. Gaussian priors are assigned to the signal coefficients given
their state variables and the Jeffreys' noninformative prior is assigned to the
noise variance. Our signal reconstruction scheme is based on an EM iteration
that aims at maximizing the posterior distribution of the signal and its state
variables given the noise variance. We construct the missing data for the EM
iteration so that the complete-data posterior distribution corresponds to a
hidden Markov tree (HMT) probabilistic graphical model that contains no loops
and implement its maximization (M) step via a max-product algorithm. This EM
algorithm estimates the vector of state variables as well as solves iteratively
a linear system of equations to obtain the corresponding signal estimate. We
select the noise variance so that the corresponding estimated signal and state
variables obtained upon convergence of the EM iteration have the largest
marginal posterior distribution. We compare the proposed and existing
state-of-the-art reconstruction methods via signal and image reconstruction
experiments.Comment: To appear in IEEE Transactions 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 reconstruction using Expectation Propagation
Many interesting problems in fields ranging from telecommunications to
computational biology can be formalized in terms of large underdetermined
systems of linear equations with additional constraints or regularizers. One of
the most studied ones, the Compressed Sensing problem (CS), consists in finding
the solution with the smallest number of non-zero components of a given system
of linear equations for known
measurement vector and sensing matrix . Here, we
will address the compressed sensing problem within a Bayesian inference
framework where the sparsity constraint is remapped into a singular prior
distribution (called Spike-and-Slab or Bernoulli-Gauss). Solution to the
problem is attempted through the computation of marginal distributions via
Expectation Propagation (EP), an iterative computational scheme originally
developed in Statistical Physics. We will show that this strategy is
comparatively more accurate than the alternatives in solving instances of CS
generated from statistically correlated measurement matrices. For computational
strategies based on the Bayesian framework such as variants of Belief
Propagation, this is to be expected, as they implicitly rely on the hypothesis
of statistical independence among the entries of the sensing matrix. Perhaps
surprisingly, the method outperforms uniformly also all the other
state-of-the-art methods in our tests.Comment: 20 pages, 6 figure
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
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
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