Frame coherence and nearly orthogonal lattices (Lenny Fukshansky, CMC)

A frame in a Euclidean space is a spanning set, which can be overdetermined. Large frames are used for redundant signal transmission, which allows for error correction. An important parameter of frames is coherence, which is maximal absolute value of the cosine of the angle between two frame vectors: the smaller it is, the closer is the frame to being orthogonal, which minimizes noise from overlapping frequencies in transmission. One good source frames with sufficiently low coherence comes from layers of minimal vectors in a lattice. We will discuss a particular class of so-called nearly orthogonal lattices, which exhibits some interesting properties from the stand-point of coherence and other related optimization problems. This is joint work with David Kogan (CGU).