4,611 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
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
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