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Activity Number: 488 - Novel Methods for Unique Spatial Imaging Applications
Type: Contributed
Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics in Imaging
Abstract #322714
Title: A Constructive Method for the Construction of Mercedes-Benz Frames in R^M
Author(s): Ghanshyam Bhatt*
Companies: Tennessee State University
Keywords: Tight frames; Equiangular tight frame ; Mercedes-Benz frame; Welch bound

A set of lines through the origin in an Euclidean space is equiangular when any pair of lines from this set intersects with each other at a common angle. This set forms an equiangular tight frame if this angle attains its value given by the Welch bound. The Mercedes-Benz frames in $\Bbb R^m,$ which are special cases of equiangular tight frames, are known to exist. They are presented here by a direct constructive method unlike previously known induction methods or the use of signature matrices. Being full spark frames, they are simplices in R^m. too. The constructive method presented thus constructs simplices in any dimension.

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