In this talk we attempt to synthesize recent progress made in the
mathematical and electrical engineering communities on topics in Clifford analysis
and the processing of color images (for example) respectively. We'll discuss
higher dimensional versions of familiar topics such as the Fourier transform,
analyticity, instantaneous frequency, analytic extensions, Hardy spaces, Hilbert
transforms, Cauchy integrals and continuous wavelet transforms. Emphasis will
be placed on the two-dimensional setting where the appropriate underlying
Clifford algebra is the set of quaternions. We'll conclude with some results and
problems in the construction of discrete wavelet bases for Clifford-valued signals.