Department of Mathematics


Tight Frames and their Symmetries

If the one of the two cartesian coordinates of a battleship is lost, then its position can no longer be determined.

It is possible to give three coordinates, so that its position can still be determined if one is lost (this is more efficient than repeating both coordinates twice). This is an example of what is called a tight frame.

In addition to obvious applications to signal analysis, such as transmission which is robust with respect to erasures (loss of information), these tight frames offer natural generalisations of orthonormal bases which reflect
additional symmetries of the space. The student uses MAGMA to construct and analyse some classes of tight frames which arise as the orbits of groups, and have numerous applications including making optimal quantum measurements.

This is an ongoing project which has led to publications with summer students (Richard Vale, Nick Hay and Helen Broome) in the past.

Researchers at The University of Auckland