Quaternions

The use of complex numbers allows for a compact notation in many areas such as in baseband representation of communication systems. Quaternions constitute a further step: they are four-dimensional hypercomplex numbers. Quaternions have already found applications in image processing, wind modeling, processing of polarized waves, and design of space-time block codes.

Papers

• Javier Vía, Daniel P. Palomar, Luis Vielva, and Ignacio Santamaría, “Quaternion ICA from Second-Order Statistics,” IEEE Trans. on Signal Processing, vol. 59, no. 4, pp. 1586-1600, April 2011.
• Javier Vía, Daniel P. Palomar, and Luis Vielva, “Generalized Likelihood Ratios for Testing the Properness of Quaternion Gaussian Vectors,” IEEE Trans. on Signal Processing, vol. 59, no. 4, pp. 1356-1370, April 2011.