Blind Multilinear Identification

We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible. These instances include: 1) closely located or highly correlated sources in antenna array processing; 2) highl...

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Bibliographic Details
Published in:IEEE transactions on information theory 2014-02, Vol.60 (2), p.1260-1280
Main Authors: Lek-Heng Lim, Comon, Pierre
Format: Article
Language:English
Subjects:
Antenna arrays
Antennas
Applied sciences
Approximation
Approximation methods
array signal processing
Blinds
channel estimation
Code Division Multiple Access
Coherence
Communication channels
Computer Science
Correlation
Detection, estimation, filtering, equalization, prediction
Engineering Sciences
Exact sciences and technology
Fluorescence
function approximation
greedy algorithms
harmonic analysis
Hilbert space
Information processing
Information theory
Information, signal and communications theory
Inverse problems
Mathematical analysis
Matrix decomposition
Miscellaneous
Radiocommunications
remote sensing
Signal and communications theory
Signal and Image Processing
Signal processing
Signal, noise
Singular value decomposition
Source separation
system identification
Telecommunications
Telecommunications and information theory
Tensile stress
Vectors
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Summary:We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible. These instances include: 1) closely located or highly correlated sources in antenna array processing; 2) highly correlated spreading codes in code division multiple access (CDMA) radio communication; and 3) nearly dependent spectra in fluorescence spectroscopy. These have important implications. In the case of antenna array processing, it allows for joint localization and extraction of multiple sources from the measurement of a noisy mixture recorded on multiple sensors in an entirely deterministic manner. In the case of CDMA, it allows the possibility of having a number of users larger than the spreading gain. In the case of fluorescence spectroscopy, it allows for detection of nearly identical chemical constituents. The proposed technique involves the solution of a bounded coherence low-rank multilinear approximation problem. We show that bounded coherence allows us to establish existence and uniqueness of the recovered solution. We will provide some statistical motivation for the approximation problem and discuss greedy approximation bounds. To provide the theoretical underpinnings for this technique, we develop a corresponding theory of sparse separable decompositions of functions, including notions of rank and nuclear norm that can be specialized to the usual ones for matrices and operators and also be applied to hypermatrices and tensors.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2291876