Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case

By Thomas Bülow, G. Sommer. IEEE Transactions on Signal Processing, 2001

394 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology, Signal Processing

View Paper: https://www.semanticscholar.org/paper/f412c313c57516619445a79391d56a7098ca8ef8

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In Computer Vision and Pattern Recognition

In Media Technology

In Signal Processing

Citations in the corpus

The Class of Clifford-Fourier Transforms (2011, background): “[8, 14, 15, 16, 18]) but also from a purely mathematical point of view (see e.”
Recent multiscale AM-FM methods in emerging applications in medical imaging (2012, methodology): “Other related work on image demodulation based on the Riesz transform extension has been reported by Mellor, Noble, Hahn, Felsberg, Sommer and collaborators in [48,52-57].”
Quaternion-MUSIC for vector-sensor array processing (2006, methodology): “A hypercomplex version of the multidimensional comple x signals [7] was also proposed by Bülow and Sommer [8].”
A Unified Theory for Steerable and Quadrature Filters (2006, methodology): “Large efforts have been made to generalize the analytic signal (Bülow and Sommer, 2001; Granlund and Knutsson, 1995) to the 2D case by projecting the scalar valued Hilbert transformation in the two dimensional space.”
Hypercomplex Fourier Transforms of Color Images (2001, background): “Bülow and Sommer have published work on hypercomplex Fourier transforms applied to grayscale images [5]–[8].”
Texture analysis based on local analysis of the Bidimensional Empirical Mode Decomposition (2005, background): “Different approaches to an nD-analytic or complex signal have been proposed in the past: • the Total Hilbert Transform [83], • the Partial Hilbert Transform [32], • the Total Complex Signal [33], • the Hypercomplex Signal [10].”
Deep Quaternion Networks (2017, methodology): “Bulow and Sommer [12] used the higher complexity representation of quaternions by extending Gabor’s complex signal”
The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes (2009, methodology): “Within the image and signal processing community, Pei and Cheng employed quaternions to process color images [17], Toyoshima implemented efficient hyper-complex digital filters [18], Bülow and Sommer used a hyper-complex representation in texture segmentation [19], whereas Zarzoso utilized…”