Gradient Flows for Frame Potentials on the Wasserstein Space

2018/08/28 by Clare Wickman, Kasso A. Okoudjou, Wickman, Clare +1
Mathematics · #42C15 #60D05 #94A12 #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1808.09319

openalex publication_date 2018/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory and optimal transport, using the methods of the second to answer questions posed in the first. In particular, we construct gradient flows in the Wasserstein space P₂(ℝ^d) for a new potential, the tightness potential, which is a modification of the probabilistic frame potential. It is shown that the potential is suited for the application of a gradient descent scheme from optimal transport that can be used as the basis of an algorithm to evolve an existing frame toward a tight probabilistic frame.

Citations

• The geometry of optimal transportation

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