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

By Soo-Chang Pei, Jian-Jiun Ding, Ja-Han Chang. IEEE Transactions on Signal Processing, 2001

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A Novel Multiresolution Spatiotemporal Saliency Detection Model and Its Applications in Image and Video Compression (2010, methodology): “Later, Pei et al. proposed an efﬁcient implementation of QFT [31] by using the transform deﬁned in [32].”
Hypercomplex Fourier Transforms of Color Images (2001, methodology): “, using the transform defined in [9], published work on the efficiency of the computation of quaternion Fourier transforms and on linear quaternion filters [10].”
The Uncertainty Principle for the Two-Sided Quaternion Fourier Transform (2017, methodology): “Derivative theorem (QFT) [1, Thm 2.10] If f, ∂ m+n ∂mx1 ∂nx2 f ∈ L2 (R2,H) for m,n ∈ N then F{ ∂m+n ∂mx1 ∂nx2 f(x)}(ξ)=(2π)m+n(iξ1) mF{f(x)}(ξ) (jξ2)n. Lemma 3.5.”
The η-bihermitian solution to a system of real quaternion matrix equations (2014, unknown): “[5–10]).”