Fourier transforms of colour images : the quaternion FFT

A discrete two-dimensional Fourier transform is presented, based on quaternion numbers (a generalisation of the complex numbers with three imaginary components). This transform allows a colour image in, say, RGB format, to be transformed as a whole, rather than as separate color components. Quaternion numbers are briefly reviewed, the transform is defined, and its two-dimensional cosinusoidal basis functions. The paper concludes with a discussion of a known problem with the transform : that a reversed image does not have a conjugate transform.