545 research outputs found
Bayesian compressive sensing framework for spectrum reconstruction in Rayleigh fading channels
Compressive sensing (CS) is a novel digital signal processing technique that has found great interest in
many applications including communication theory and wireless communications. In wireless communications, CS
is particularly suitable for its application in the area of spectrum sensing for cognitive radios, where the complete
spectrum under observation, with many spectral holes, can be modeled as a sparse wide-band signal in the frequency
domain. Considering the initial works performed to exploit the benefits of Bayesian CS in spectrum sensing, the fading
characteristic of wireless communications has not been considered yet to a great extent, although it is an inherent feature
for all sorts of wireless communications and it must be considered for the design of any practically viable wireless system.
In this paper, we extend the Bayesian CS framework for the recovery of a sparse signal, whose nonzero coefficients follow
a Rayleigh distribution. It is then demonstrated via simulations that mean square error significantly improves when
appropriate prior distribution is used for the faded signal coefficients and thus, in turns, the spectrum reconstruction
improves. Different parameters of the system model, e.g., sparsity level and number of measurements, are then varied
to show the consistency of the results for different cases
A Noise-Robust Fast Sparse Bayesian Learning Model
This paper utilizes the hierarchical model structure from the Bayesian Lasso
in the Sparse Bayesian Learning process to develop a new type of probabilistic
supervised learning approach. The hierarchical model structure in this Bayesian
framework is designed such that the priors do not only penalize the unnecessary
complexity of the model but will also be conditioned on the variance of the
random noise in the data. The hyperparameters in the model are estimated by the
Fast Marginal Likelihood Maximization algorithm which can achieve sparsity, low
computational cost and faster learning process. We compare our methodology with
two other popular learning models; the Relevance Vector Machine and the
Bayesian Lasso. We test our model on examples involving both simulated and
empirical data, and the results show that this approach has several performance
advantages, such as being fast, sparse and also robust to the variance in
random noise. In addition, our method can give out a more stable estimation of
variance of random error, compared with the other methods in the study.Comment: 15 page
Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been
used to model sparsity-inducing priors that realize a class of concave penalty
functions for the regression task in real-valued signal models. Motivated by
the relative scarcity of formal tools for SBL in complex-valued models, this
paper proposes a GSM model - the Bessel K model - that induces concave penalty
functions for the estimation of complex sparse signals. The properties of the
Bessel K model are analyzed when it is applied to Type I and Type II
estimation. This analysis reveals that, by tuning the parameters of the mixing
pdf different penalty functions are invoked depending on the estimation type
used, the value of the noise variance, and whether real or complex signals are
estimated. Using the Bessel K model, we derive a sparse estimator based on a
modification of the expectation-maximization algorithm formulated for Type II
estimation. The estimator includes as a special instance the algorithms
proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results
show the superiority of the proposed estimator over these state-of-the-art
estimators in terms of convergence speed, sparseness, reconstruction error, and
robustness in low and medium signal-to-noise ratio regimes.Comment: The paper provides a new comprehensive analysis of the theoretical
foundations of the proposed estimators. Minor modification of the titl
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
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