Papers › Method of Moments for Estimation of Noisy Curves
Method of Moments for Estimation of Noisy Curves
Phillip Lo, Yuehaw Khoo
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In this paper, we study the problem of recovering a ground truth high dimensional piecewise linear curve C^*(t):[0, 1]→ℝᵈ from a high noise Gaussian point cloud with covariance σ²I centered around the curve. We establish that the sample complexity of recovering C^* from data scales with order at least σ⁶. We then show that recovery of a piecewise linear curve from the third moment is locally well-posed, and hence O(σ⁶) samples is also sufficient for recovery. We propose methods to recover a curve from data based on a fitting to the third moment tensor with a careful initialization strategy and conduct some numerical experiments verifying the ability of our methods to recover curves. All code for our numerical experiments is publicly available on GitHub.
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