Grassmannian Frame Computation via Accelerated Alternating Projections

Bastien Massion, Estelle Massart

Session: Optimal frames and codes (Dustin Mixon, Matthew Fickus)

Keywords: Mutual Coherence, Grassmannian frame, line packing, Gram matrix, Accelerated Alternating Projections

Abstract: This paper addresses the approximation of real and complex Grassmannian frames, namely sets of unit-norm vectors with minimum mutual coherence. We recast this problem as a collection of feasibility problems aiming to design frames with given target coherence, that evolves during the execution of the algorithm. The feasibility problems are solved by an accelerated alternating projection algorithm, leveraging a Gram matrix representation of the frames. Numerical experiments indicate that our proposed Targeted coherence with Accelerated Alternating Projection (TAAP) algorithm outperforms state-of-the-art methods regarding the mutual coherence vs computational cost criterion, exhibiting the largest improvement over existing methods when the frame dimension is comparable to the dimension of the ambient space.

Submission Number: 79