31,925 research outputs found
Blind separation of noisy multivariate data using second-order statistics
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (leaves 81-83).A second-order method for blind source separation of noisy instantaneous linear mixtures is presented and analyzed for the case where the signal order k and noise covariance GG-H are unknown. Only a data set X of dimension n > k and of sample size m is observed, where X = AP + GW. The quality of separation depends on source-observation ratio k/n, the degree of spectral diversity, and the second-order non-stationarity of the underlying sources. The algorithm estimates the Second-Order separation transform A, the signal Order, and Noise, and is therefore referred to as SOON. SOON iteratively estimates: 1) k using a scree metric, and 2) the values of AP, G, and W using the Expectation-Maximization (EM) algorithm, where W is white noise and G is diagonal. The final step estimates A and the set of k underlying sources P using a variant of the joint diagonalization method, where P has k independent unit-variance elements. Tests using simulated Auto Regressive (AR) gaussian data show that SOON improves the quality of source separation in comparison to the standard second-order separation algorithms, i.e., Second-Order Blind Identification (SOBI) [3] and Second-Order Non-Stationary (SONS) blind identification [4]. The sensitivity in performance of SONS and SOON to several algorithmic parameters is also displayed in these experiments. To reduce sensitivities in the pre-whitening step of these algorithms, a heuristic is proposed by this thesis for whitening the data set; it is shown to improve separation performance. Additionally the application of blind source separation techniques to remote sensing data is discussed.(cont.) Analysis of remote sensing data collected by the AVIRIS multichannel visible/infrared imaging instrument shows that SOON reveals physically significant dynamics within the data not found by the traditional methods of Principal Component Analysis (PCA) and Noise Adjusted Principal Component Analysis (NAPCA).by Keith Herring.S.M
Multi-Detector Multi-Component spectral matching and applications for CMB data analysis
We present a new method for analyzing multi--detector maps containing
contributions from several components. Our method, based on matching the data
to a model in the spectral domain, permits to estimate jointly the spatial
power spectra of the components and of the noise, as well as the mixing
coefficients. It is of particular relevance for the analysis of
millimeter--wave maps containing a contribution from CMB anisotropies.Comment: 15 pages, 7 Postscript figures, submitted to MNRA
Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation
This paper concerns underdetermined linear instantaneous and convolutive
blind source separation (BSS), i.e., the case when the number of observed mixed
signals is lower than the number of sources.We propose partial BSS methods,
which separate supposedly nonstationary sources of interest (while keeping
residual components for the other, supposedly stationary, "noise" sources).
These methods are based on the general differential BSS concept that we
introduced before. In the instantaneous case, the approach proposed in this
paper consists of a differential extension of the FastICA method (which does
not apply to underdetermined mixtures). In the convolutive case, we extend our
recent time-domain fast fixed-point C-FICA algorithm to underdetermined
mixtures. Both proposed approaches thus keep the attractive features of the
FastICA and C-FICA methods. Our approaches are based on differential sphering
processes, followed by the optimization of the differential nonnormalized
kurtosis that we introduce in this paper. Experimental tests show that these
differential algorithms are much more robust to noise sources than the standard
FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for
linear instantaneous and convolutive underdetermined mixture
Joint Tensor Factorization and Outlying Slab Suppression with Applications
We consider factoring low-rank tensors in the presence of outlying slabs.
This problem is important in practice, because data collected in many
real-world applications, such as speech, fluorescence, and some social network
data, fit this paradigm. Prior work tackles this problem by iteratively
selecting a fixed number of slabs and fitting, a procedure which may not
converge. We formulate this problem from a group-sparsity promoting point of
view, and propose an alternating optimization framework to handle the
corresponding () minimization-based low-rank tensor
factorization problem. The proposed algorithm features a similar per-iteration
complexity as the plain trilinear alternating least squares (TALS) algorithm.
Convergence of the proposed algorithm is also easy to analyze under the
framework of alternating optimization and its variants. In addition,
regularization and constraints can be easily incorporated to make use of
\emph{a priori} information on the latent loading factors. Simulations and real
data experiments on blind speech separation, fluorescence data analysis, and
social network mining are used to showcase the effectiveness of the proposed
algorithm
SZ and CMB reconstruction using Generalized Morphological Component Analysis
In the last decade, the study of cosmic microwave background (CMB) data has
become one of the most powerful tools to study and understand the Universe.
More precisely, measuring the CMB power spectrum leads to the estimation of
most cosmological parameters. Nevertheless, accessing such precious physical
information requires extracting several different astrophysical components from
the data. Recovering those astrophysical sources (CMB, Sunyaev-Zel'dovich
clusters, galactic dust) thus amounts to a component separation problem which
has already led to an intense activity in the field of CMB studies. In this
paper, we introduce a new sparsity-based component separation method coined
Generalized Morphological Component Analysis (GMCA). The GMCA approach is
formulated in a Bayesian maximum a posteriori (MAP) framework. Numerical
results show that this new source recovery technique performs well compared to
state-of-the-art component separation methods already applied to CMB data.Comment: 11 pages - Statistical Methodology - Special Issue on Astrostatistics
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