SVD and signal processing: algorithms, applications and architectures
SVD and signal processing: algorithms, applications and architectures
The SVD and reduced rank signal processing
Signal Processing - Theme issue on singular value decomposition
Hypercomplex spectral transformations
Hypercomplex spectral transformations
Spatial—color Clifford algebras for invariant image recognition
Geometric computing with Clifford algebras
SVD and Signal Processing II: Algorithms, Analysis and Applications
SVD and Signal Processing II: Algorithms, Analysis and Applications
SVD and Signaling Processing III: Algorithms, Architectures, and Applications
SVD and Signaling Processing III: Algorithms, Architectures, and Applications
Microwave Mobile Communications
Microwave Mobile Communications
Analysis of a polarized seismic wave model
IEEE Transactions on Signal Processing
Wideband spectral matrix filtering for multicomponent sensors array
Signal Processing
Simultaneous real diagonalization of rectangular quaternionic matrix pairs and its algorithm
Computers & Mathematics with Applications
The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
IEEE Transactions on Signal Processing
Quad-quaternion music for DOA estimation using electromagnetic vector sensors
EURASIP Journal on Advances in Signal Processing
Empirical mode decomposition for trivariate signals
IEEE Transactions on Signal Processing
Properness and widely linear processing of quaternion random vectors
IEEE Transactions on Information Theory
Augmented second-order statistics of quaternion random signals
Signal Processing
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Prediction of wide-sense stationary quaternion random signals
Signal Processing
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We present a new approach for vector-sensor signal modelling and processing, based on the use of quaternion algebra. We introduce the concept of quaternionic signal and give some primary tools to characterize it. We then study the problem of vector-sensor array signals, and introduce a subspace method for wave separation on such arrays. For this purpose, we expose the extension of the Singular Value Decomposition (SVD) algorithm to the field of quaternions. We discuss in more details Singular Value Decomposition for matrices of Quaternions (SVDQ) and linear algebra over quaternions field. The SVDQ allows to calculate the best rank-α approximation of a quaternion matrix and can be used in subspace method for wave separation over vector-sensor array. As the SVDQ takes into account the relationship between components, we show that SVDQ is more efficient than classical SVD in polarized wave separation problem.