Low-rank decomposition of multi-way arrays: a signal processing perspective

In many signal processing applications of linear algebra tools, the signal part of a postulated model lies in a so-called signal sub-space, while the parameters of interest are in one-to-one correspondence with a certain basis of this subspace. The signal sub-space can often be reliably estimated fr...

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Bibliographic Details
Published in2004 IEEE Sensor Array and Multichannel Signal Processing Workshop pp. 52 - 58
Main Author Sidiropoulos, N.D.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2004
Subjects
Array signal processing
Linear algebra
Magnetic analysis
Matrices
Matrix converters
Multidimensional signal processing
Signal analysis
Signal processing
Telecommunications
Video signal processing
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Summary:In many signal processing applications of linear algebra tools, the signal part of a postulated model lies in a so-called signal sub-space, while the parameters of interest are in one-to-one correspondence with a certain basis of this subspace. The signal sub-space can often be reliably estimated from measured data, but the particular basis of interest cannot be identified without additional problem-specific structure. This is a manifestation of rotational indeterminacy, i.e., non-uniqueness of low-rank matrix decomposition. The situation is very different for three-or higher-way arrays, i.e., arrays indexed by three or more independent variables, for which low-rank decomposition is unique under mild conditions. This has fundamental implications for DSP problems which deal with such data. This paper provides a brief lour of the basic elements of this theory, along with many examples of application in problems of current interest in the signal processing community.
ISBN:9780780385450
0780385454
DOI:10.1109/SAM.2004.1502907