Congruent Voronoi Tessellations from an Equiangular Frame


B. Mondal, R. Samanta and Robert W. Heath Jr.


Applied and Computational Harmonic Analysis, vol. 23, pp. 254-258, Sept. 2007.


It is proven that the Voronoi tessellations of the real projective space generated by an equiangular frame are congruent. Two implications of this result are mentioned - an equiangular frame forms the best N-point representation of an isotropically distributed one-dimensional subspace in terms of mutual information and a subspace quantizer defined by an equiangular frame provides equal partial distortion.

The initial preprint is available here. The final version is available from Applied and Computational Harmonic Analysis.