Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT

Keywords

Quaternion, Fast Fourier transform, Convolution (computer science), Quaternion algebra, Mathematics

References

• Hypercomplex Numbers: An Elementary Introduction to AlgebrasI. L. Kantor, A. S. Solodovnikov — 1989
• Colour-sensitive edge detection using hypercomplex filtersC. J. Evans, Stephen J. Sangwine, Todd A. Ell — 2000
• Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systemsTodd A. Ell — 1993
• Decomposition of 2D Hypercomplex Fourier transforms into pairs of complex fourier transformsTodd A. Ell, Stephen J. Sangwine — 2000
• The discrete quaternion Fourier transformStephen J. Sangwine — 1997
• Colour image edge detector based on quaternion convolutionStephen J. Sangwine — 1998
• Fourier transforms of colour images using quaternion or hypercomplex, numbersStephen J. Sangwine — 1996
• A novel block truncation coding of color images using a quaternion-moment-preserving principleSoo‐Chang Pei, Ching-Min Cheng — 1997
• Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric dataPierre Duhamel — 1986
• Hypercomplex color-sensitive smoothing filtersC J Evans, Stephen J. Sangwine, Todd A. Ell — 2000
• Color image processing by using binary quaternion-moment-preserving thresholding techniqueSoo‐Chang Pei, Ching-Min Cheng — 1999
• Hypercomplex Wiener-Khintchine theorem with application to color image correlationTodd A. Ell, Stephen J. Sangwine — 2000
• Hypercomplex spectral transformationsTodd A. Ell — 1992
• A novel block truncation coding of color images by using quaternion-moment-preserving principleSoo‐Chang Pei, Ching-Min Cheng — 1996
• Elements of QuaternionsWilliam Hamilton — 1969
• Hypercomplex NumbersI. L. Kantor, A. S. Solodovnikov — 1989
• Hypercomplex spectral signal representations for the processing and analysis of imagesThomas Bülow — 1999
• Multi-Dimensional Signal Processin Using an Algebraically Extended Signal RepresentationThomas Bülow, G. Sommer — 1997

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• A Novel Multiresolution Spatiotemporal Saliency Detection Model and Its Applications in Image and Video CompressionEva M. Fritz, Annemaree Carroll — 2010
• Vector Sparse Representation of Color Image Using Quaternion Matrix AnalysisDamien Kingsbury, Michael Leach — 2015
• TRANSFORMASI KANONIKAL LINEAR QUATERNION QUATERNION LINEAR CANONICAL TRANSFORMResnawati, Mawardi Bahri, Jeffry Kusuma — 2013
• Tensor transform-based quaternion fourier transform algorithmArtyom M. Grigoryan, Sos С. Agaian — 2015
• Drabinkowa struktura układu mnożenia kwaternionów: analiza i redukcja zakresu dynamicznegoMarek Parfieniuk, A. Petrovsky — 2010
• Amplitude demodulation of interferometric signals with a 2D Hilbert transformMaciek Wielgus — 2011
• Studies on complex and hypercomplex multidimensional analytic signalsKajetana M. Snopek — 2013
• Zracjonalizowany algorytm mnożenia dwóch kwaternionówA. Tariov, G. Tariova — 2010
• Tighter Uncertainty Principles Based on Quaternion Fourier TransformYan Yang, Pei Dang, Tao Qian — 2016
• 2D quaternion Fourier spectral analysis and its applicationsJa-Han Chang, Soo‐Chang Pei, Jian–Jiun Ding — 2004
• Classification of color textures by Gabor filteringChristoph Palm, Thomas Lehmann — 2002
• Aplicación de los números hipercomplejos o cuaterniones en imágenes de colorVivianne A Mahecha — 2008
• Aspekty algorytmiczne redukcji liczby bloków mnożących w układzie do obliczania iloczynu dwóch kwaternionówG. Tariova, A. Tariov — 2010
• Connecting spatial and frequency domains for the quaternion Fourier transformHendrik De Bie, Nele De Schepper, Todd A. Ell — 2015
• Quaternion matrix singular value decomposition and its applications for color image processingSoo-ChangPei, Ja-Han Chang, Jian–Jiun Ding — 2003
• Color image registration via quaternion Fourier transform and parametric template methodJ. Pan, Shumin Fei, Wenlin Zou — 2010
• The η-bihermitian solution to a system of real quaternion matrix equationsZhuo‐Heng He, Qing‐Wen Wang — 2014
• Towards realtime measurement of connectedness in human movementMichael Krzyżaniak, Rushil Anirudh, Vinay Venkataraman — 2015
• Quaternion Fourier-Mellin moments for color imagesLiqiang Guo, Ming Zhu — 2011
• Quaternion gyrator transform and its application to color image encryptionZhuhong Shao, Jiasong Wu, Jean-Louis Coatrieux — 2013

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