Quaternion-MUSIC for vector-sensor array processing

Miron, Sébastian; Bihan, Nicolas Le; Mars, Jérôme

doi:10.1109/tsp.2006.870630

Cited by 292 publications

(202 citation statements)

References 29 publications

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“…Quaternions have found applications in computer graphics, for the modelling of three-dimensional (3-D) rotations [6], in robotics [7], molecular modelling [8], processing colour images [9], hyper-complex digital filters [10], texture segmentation [11], source separation [12], watermarking [13], spectrum estimation [14] quaternion singular value decomposition and in the MUSIC algorithm to process polarized waves [15], [16], quaternion least squares [8], [17], and quaternion singular spectrum analysis [18]. In [4] the formulation for a quaternion LMS adaptive filtering has also been provided and used for the processing of quaternion valued signals.…”

Section: Introductionmentioning

confidence: 99%

Quaternion adaptive line enhancer

Sanei

Took

Enshaeifar

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-The recovery of periodic signals from their noisy single channel mixtures has made wide use of the adaptive line enhancer (ALE). The ALE, however, is not designed for detection of two-(2-D) or three-dimensional (3-D) periodic signals such as tremor in an unconstrained hand motion. An ALE which can perform restoration of 3-D periodic signals is therefore required for such purposes. These signals may not exhibit periodicity in a single dimension. To address and solve this problem a quaternion adaptive line enhancer (QALE) is introduced in this paper for the first time which exploits the quaternion least mean square (QLMS) algorithm for the detection of 3-D (extendable to 4-D) periodic signals.Index Terms-ALE, quaternion adaptive line enhancer, QLMS, quaternion shift.

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Section: Introductionmentioning

confidence: 99%

Quaternion adaptive line enhancer

Sanei

Took

Enshaeifar

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…Multidimensional (m-D) signal processing has a variety of applications and the modeling of multiple variables is carried out traditionally within the real-valued matrix algebra, while in recent years we have observed the successful exploitation of hypercomplex numbers in areas including colour image processing (Pei and Cheng, 1999;Pei et al, 2004;Sangwine and Ell, 2000;Parfieniuk and Petrovsky, 2010;Ell et al, 2014;Liu et al, 2014), vector-sensor array processing (Le Bihan and Mars, 2004;Miron et al, 2006;Le Bihan et al, 2007;Tao, 2013;Tao and Chang, 2014;Zhang et al, 2014;Hawes and Liu, 2015;Jiang et al, 2016a,b), and quaternion-valued wireless communications (Zetterberg and Brandstrom, 1977;Isaeva and Sarytchev, 1995;Liu, 2014). The most widely used hypercomplex numbers are quaternions, with rigorous physical interpretation for 3-D and 4-D rotational problems (Kantor et al, 1989;Ward, 1997).…”

Section: Introductionmentioning

confidence: 99%

Filtering and tracking with trinion-valued adaptive algorithms

Gou

Liu

et al. 2016

Frontiers Inf Technol Electronic Eng

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A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared with the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind recordings and synthetic data sets are provided to demonstrate the potentials of this new modeling method.

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“…Hypercomplex number systems proved useful due to their use in operations such as Discrete Fourier Transform, convolution, correlation and filtering of one-, two-and higher-dimensional signals [1-3, 5, 7, 11, 15, 18-21, 27]. "There are already many publications available on the use of hypercomplex numbers in image recognition including face recognition [17,28] as well as audio signal recognition [14]. Wider and wider application of hypercomplex number systems can be found during the organization of data transmission channels on the base of MIMO technology (multiple input-multiple output) and also for the newest techniques of space time coding [4,6].…”

Section: Introductionmentioning

confidence: 99%