On Nearly Orthogonal Lattice Bases

We study ”nearly orthogonal” lattice bases, or bases where the angle between any basis vector and the linear space spanned by the other basis vectors is greater than 3 radians. We show that a nearly orthogonal lattice basis always contains a shortest lattice vector. Also, if the basis vectors have lengths within a certain constant factor of one another (that is, they 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.

By: Ramesh Neelamani; Richard G. Baraniuk; Sanjeeb Dash

Published in: RC23620 in 2005


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