Probabilistic Dual Frames and Minimization of Dual Frame Potentials

2025/02/25 by Dongwei Chen, Chen, Dongwei
Decision Sciences · Engineering · Environmental Science · #42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Probabilistic and Robust Engineering Design #Structural Analysis and Optimization #Wind and Air Flow Studies

paper · pdf · doi:10.48550/arxiv.2502.17760

openalex publication_date 2025/02/25 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

This paper studies probabilistic dual frames and the associated dual frame potentials from the perspective of optimal mass transport. The main contribution of this work shows that given a probabilistic frame, its associated dual frame potential is minimized if and only if the probabilistic frame is tight and the probabilistic dual frame is the canonical dual. In particular, the tightness condition can be dropped if the probabilistic dual frame potential is minimized only among probabilistic dual frames of pushforward type.

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• Duality and Geodesics for Probabilistic Frames
• Approximately Dual and Pseudo-Dual Probabilistic Frames
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