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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Revisiting the Kronecker Array Transform

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Author(s):
Masiero, Bruno ; Nascimento, Vitor H.
Total Authors: 2
Document type: Journal article
Source: IEEE SIGNAL PROCESSING LETTERS; v. 24, n. 5, p. 525-529, MAY 2017.
Web of Science Citations: 2
Abstract

It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. (AU)

FAPESP's process: 14/04256-2 - Low-cost algorithms for parameter estimation
Grantee:Vitor Heloiz Nascimento
Support type: Regular Research Grants
FAPESP's process: 14/06066-6 - Construction, Calibration and Experimental Verification of a Microphone Array with Separable Geometry
Grantee:Bruno Sanches Masiero
Support type: Scholarships in Brazil - Post-Doctorate