The Complexity of the Quaternion Product
The Complexity of the Quaternion Product
The Theory and Use of the Quaternion Wavelet Transform
Journal of Mathematical Imaging and Vision
Quaternion wavelet phase based stereo matching for uncalibrated images
Pattern Recognition Letters
Quaternionic lattice structures for four-channel paraunitary filter banks
EURASIP Journal on Applied Signal Processing
IEEE Transactions on Signal Processing
Integer fast Fourier transform
IEEE Transactions on Signal Processing
Hypercomplex correlation techniques for vector images
IEEE Transactions on Signal Processing
Multiple Multidimensional Morse Wavelets
IEEE Transactions on Signal Processing
The Theory of Quaternion Orthogonal Designs
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Hypercomplex signals-a novel extension of the analytic signal tothe multidimensional case
IEEE Transactions on Signal Processing
Color Image Watermarking Using Multidimensional Fourier Transforms
IEEE Transactions on Information Forensics and Security
Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets
IEEE Transactions on Image Processing
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A lifting-based structure for quaternion multipliers with unit-magnitude constant coefficients is proposed, whose development was inspired by the well-known implementation of a plane rotation (complex multiplication with a unit-magnitude coefficient) using three shears each of which corresponds to one real multiplication and addition. Our solution is mainly aimed at implementing quaternion transforms as dedicated multiplierless digital circuits. Compared to alternative schemes obtained using the most known general-purpose lifting factorizations, it needs 1/3-1/5 less lifting steps. On general-purpose hardware, it allows for saving 14% operations at the price of representing the hypercomplex coefficient indirectly using six, instead of four, real numbers.