2023/04/23 by Ruiyu Han, Han, Ruiyu, Dejan Slepčev +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Fibromyalgia and Chronic Fatigue Syndrome Research #Metric Geometry (math.MG) #Myofascial pain diagnosis and treatment #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2304.11538
openalex publication_date 2023/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In order to compare and interpolate signals, we investigate a Riemannian geometry on the space of signals. The metric allows discontinuous signals and measures both horizontal (thus providing many benefits of the Wasserstein metric) and vertical deformations. Moreover, it allows for signed signals, which overcomes the main deficiency of optimal transportation-based metrics in signal processing. We characterize the metric properties of the space of signals and establish the regularity and stability of geodesics. Furthermore, we introduce an efficient numerical scheme to compute the geodesics and present several experiments which highlight the nature of the metric.