Grassmannian Frame Computation via Accelerated Alternating Projections

Massion, Bastien;Massart, Estelle
(2025) Sampling Theory and Applications — Location: Vienna (28.July.2025)

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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-ofthe-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.
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Massion, B., & Massart, E. (2025). Grassmannian Frame Computation via Accelerated Alternating Projections. Proceedings of the International Conference on Sampling Theory and Applications. Published. Sampling Theory and Applications, Vienna. https://doi.org/10.1109/SampTA64769.2025.11133550 (Original work published 2025)