9,361 research outputs found
Bayesian Hypothesis Testing for Block Sparse Signal Recovery
This letter presents a novel Block Bayesian Hypothesis Testing Algorithm
(Block-BHTA) for reconstructing block sparse signals with unknown block
structures. The Block-BHTA comprises the detection and recovery of the
supports, and the estimation of the amplitudes of the block sparse signal. The
support detection and recovery is performed using a Bayesian hypothesis
testing. Then, based on the detected and reconstructed supports, the nonzero
amplitudes are estimated by linear MMSE. The effectiveness of Block-BHTA is
demonstrated by numerical experiments.Comment: 5 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1412.231
Conditioning of Random Block Subdictionaries with Applications to Block-Sparse Recovery and Regression
The linear model, in which a set of observations is assumed to be given by a
linear combination of columns of a matrix, has long been the mainstay of the
statistics and signal processing literature. One particular challenge for
inference under linear models is understanding the conditions on the dictionary
under which reliable inference is possible. This challenge has attracted
renewed attention in recent years since many modern inference problems deal
with the "underdetermined" setting, in which the number of observations is much
smaller than the number of columns in the dictionary. This paper makes several
contributions for this setting when the set of observations is given by a
linear combination of a small number of groups of columns of the dictionary,
termed the "block-sparse" case. First, it specifies conditions on the
dictionary under which most block subdictionaries are well conditioned. This
result is fundamentally different from prior work on block-sparse inference
because (i) it provides conditions that can be explicitly computed in
polynomial time, (ii) the given conditions translate into near-optimal scaling
of the number of columns of the block subdictionaries as a function of the
number of observations for a large class of dictionaries, and (iii) it suggests
that the spectral norm and the quadratic-mean block coherence of the dictionary
(rather than the worst-case coherences) fundamentally limit the scaling of
dimensions of the well-conditioned block subdictionaries. Second, this paper
investigates the problems of block-sparse recovery and block-sparse regression
in underdetermined settings. Near-optimal block-sparse recovery and regression
are possible for certain dictionaries as long as the dictionary satisfies
easily computable conditions and the coefficients describing the linear
combination of groups of columns can be modeled through a mild statistical
prior.Comment: 39 pages, 3 figures. A revised and expanded version of the paper
published in IEEE Transactions on Information Theory (DOI:
10.1109/TIT.2015.2429632); this revision includes corrections in the proofs
of some of the result
Spatiotemporal Sparse Bayesian Learning with Applications to Compressed Sensing of Multichannel Physiological Signals
Energy consumption is an important issue in continuous wireless
telemonitoring of physiological signals. Compressed sensing (CS) is a promising
framework to address it, due to its energy-efficient data compression
procedure. However, most CS algorithms have difficulty in data recovery due to
non-sparsity characteristic of many physiological signals. Block sparse
Bayesian learning (BSBL) is an effective approach to recover such signals with
satisfactory recovery quality. However, it is time-consuming in recovering
multichannel signals, since its computational load almost linearly increases
with the number of channels.
This work proposes a spatiotemporal sparse Bayesian learning algorithm to
recover multichannel signals simultaneously. It not only exploits temporal
correlation within each channel signal, but also exploits inter-channel
correlation among different channel signals. Furthermore, its computational
load is not significantly affected by the number of channels. The proposed
algorithm was applied to brain computer interface (BCI) and EEG-based driver's
drowsiness estimation. Results showed that the algorithm had both better
recovery performance and much higher speed than BSBL. Particularly, the
proposed algorithm ensured that the BCI classification and the drowsiness
estimation had little degradation even when data were compressed by 80%, making
it very suitable for continuous wireless telemonitoring of multichannel
signals.Comment: Codes are available at:
https://sites.google.com/site/researchbyzhang/stsb
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