7,843 research outputs found
A simple and objective method for reproducible resting state network (RSN) detection in fMRI
Spatial Independent Component Analysis (ICA) decomposes the time by space
functional MRI (fMRI) matrix into a set of 1-D basis time courses and their
associated 3-D spatial maps that are optimized for mutual independence. When
applied to resting state fMRI (rsfMRI), ICA produces several spatial
independent components (ICs) that seem to have biological relevance - the
so-called resting state networks (RSNs). The ICA problem is well posed when the
true data generating process follows a linear mixture of ICs model in terms of
the identifiability of the mixing matrix. However, the contrast function used
for promoting mutual independence in ICA is dependent on the finite amount of
observed data and is potentially non-convex with multiple local minima. Hence,
each run of ICA could produce potentially different IC estimates even for the
same data. One technique to deal with this run-to-run variability of ICA was
proposed by Yang et al. (2008) in their algorithm RAICAR which allows for the
selection of only those ICs that have a high run-to-run reproducibility. We
propose an enhancement to the original RAICAR algorithm that enables us to
assign reproducibility p-values to each IC and allows for an objective
assessment of both within subject and across subjects reproducibility. We call
the resulting algorithm RAICAR-N (N stands for null hypothesis test), and we
have applied it to publicly available human rsfMRI data (http://www.nitrc.org).
Our reproducibility analyses indicated that many of the published RSNs in
rsfMRI literature are highly reproducible. However, we found several other RSNs
that are highly reproducible but not frequently listed in the literature.Comment: 54 pages, 13 figure
Bayesian orthogonal component analysis for sparse representation
This paper addresses the problem of identifying a lower dimensional space
where observed data can be sparsely represented. This under-complete dictionary
learning task can be formulated as a blind separation problem of sparse sources
linearly mixed with an unknown orthogonal mixing matrix. This issue is
formulated in a Bayesian framework. First, the unknown sparse sources are
modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted
mixture of an atom at zero and a Gaussian distribution is proposed as prior
distribution for the unobserved sources. A non-informative prior distribution
defined on an appropriate Stiefel manifold is elected for the mixing matrix.
The Bayesian inference on the unknown parameters is conducted using a Markov
chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is
designed to generate samples asymptotically distributed according to the joint
posterior distribution of the unknown model parameters and hyperparameters.
These samples are then used to approximate the joint maximum a posteriori
estimator of the sources and mixing matrix. Simulations conducted on synthetic
data are reported to illustrate the performance of the method for recovering
sparse representations. An application to sparse coding on under-complete
dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin
Efficient Blind Source Separation Algorithms with Applications in Speech and Biomedical Signal Processing
Blind source separation/extraction (BSS/BSE) is a powerful signal processing method and has been applied extensively in many fields such as biomedical sciences and speech signal processing, to extract a set of unknown input sources from a set of observations. Different algorithms of BSS were proposed in the literature, that need more investigations, related to the extraction approach, computational complexity, convergence speed, type of domain (time or frequency), mixture properties, and extraction performances. This work presents a three new BSS/BSE algorithms based on computing new transformation matrices used to extract the unknown signals. Type of signals considered in this dissertation are speech, Gaussian, and ECG signals. The first algorithm, named as the BSE-parallel linear predictor filter (BSE-PLP), computes a transformation matrix from the the covariance matrix of the whitened data. Then, use the matrix as an input to linear predictor filters whose coefficients being the unknown sources. The algorithm has very fast convergence in two iterations. Simulation results, using speech, Gaussian, and ECG signals, show that the model is capable of extracting the unknown source signals and removing noise when the input signal to noise ratio is varied from -20 dB to 80 dB. The second algorithm, named as the BSE-idempotent transformation matrix (BSE-ITM), computes its transformation matrix in iterative form, with less computational complexity. The proposed method is tested using speech, Gaussian, and ECG signals. Simulation results show that the proposed algorithm significantly separate the source signals with better performance measures as compared with other approaches used in the dissertation. The third algorithm, named null space idempotent transformation matrix (NSITM) has been designed using the principle of null space of the ITM, to separate the unknown sources. Simulation results show that the method is successfully separating speech, Gaussian, and ECG signals from their mixture. The algorithm has been used also to estimate average FECG heart rate. Results indicated considerable improvement in estimating the peaks over other algorithms used in this work
Foreground removal for Square Kilometre Array observations of the Epoch of Reionization with the Correlated Component Analysis
We apply the Correlated Component Analysis (CCA) method on simulated data of
the Square Kilometre Array, with the aim of accurately cleaning the 21 cm
reionization signal from diffuse foreground contamination. The CCA has been
developed for the Cosmic Microwave Background, but the application of the
Fourier-domain implementation of this method to the reionization signal is
straightforward.
The CCA is a parametric method to estimate the frequency behaviour of the
foregrounds from the data by using second-order statistics. We test its
performance on foreground simulations of increasing complexity, designed to
challenge the parametric models adopted. We also drop the assumption of
spectral smoothness that most of the methods rely upon. We are able to clean
effectively the simulated data across the explored frequency range (100-200
MHz) for all the foreground simulations. This shows that the CCA method is very
promising for EoR component separation.Comment: 12 pages, 15 figures, accepted by MNRA
Sparse and Non-Negative BSS for Noisy Data
Non-negative blind source separation (BSS) has raised interest in various
fields of research, as testified by the wide literature on the topic of
non-negative matrix factorization (NMF). In this context, it is fundamental
that the sources to be estimated present some diversity in order to be
efficiently retrieved. Sparsity is known to enhance such contrast between the
sources while producing very robust approaches, especially to noise. In this
paper we introduce a new algorithm in order to tackle the blind separation of
non-negative sparse sources from noisy measurements. We first show that
sparsity and non-negativity constraints have to be carefully applied on the
sought-after solution. In fact, improperly constrained solutions are unlikely
to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA
(non-negative Generalized Morphological Component Analysis), makes use of
proximal calculus techniques to provide properly constrained solutions. The
performance of nGMCA compared to other state-of-the-art algorithms is
demonstrated by numerical experiments encompassing a wide variety of settings,
with negligible parameter tuning. In particular, nGMCA is shown to provide
robustness to noise and performs well on synthetic mixtures of real NMR
spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal
Processin
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