CyFM: תרגום אופטימלי צילינדרי להתאמה של זרם רב-ערוצי

תקציר מקורי באנגליתarXiv:2609.14171v1 Announce Type: new Abstract: Complex-valued signals, such as Magnetic Resonance Imaging (MRI) and audio spectrograms, are almost always modelled as flat two-channel Euclidean data. For nonzero values the amplitude-phase chart $z \mapsto (|z|, z/|z|)$ identifies the signal domain with the cylinder $(0, \infty) \times S^1$, on which we deliberately replace the inherited metric $dA^2 + A^2 d\theta^2$ by the decoupled product metric $dA^2 + d\theta^2$. In this empirical study we measure what that substitution costs and what it buys. By computing exact analytical bridges, we demonstrate that Cartesian paths induce a heavy-tailed distribution of angular velocity (power law index $\approx 1.0$), with nearly half of the probability paths exceeding an angular speed of $\pi$ under