On Nearly Orthogonal Lattice Bases
Baraniuk, Richard G.
lattices; shortest lattice vector; orthogonality defect; JPEG; compression
We study "nearly orthogonal" lattice bases, or bases where the angle between any basis vector and the linear subspace spanned by the other basis vectors is greater than 60°. We show that a nearly orthogonal lattice basis always contains a shortest lattice vector. Moreover, if the lengths of the basis vectors are "nearly equal", then the basis is the unique nearly orthogonal lattice basis, up to multiplication of basis vectors by ±1. These results are motivated by an application involving JPEG image compression.