Abstract:We study the problem of denoising observations \(Y_i=X_i+Z_i\), where the latent variables \(X_i\) are sampled from a low-dimensional manifold in \(\mathbb{R}^n\) and the noise variables \(Z_i\) are isotropic Gaussian. We propose a convex-relaxation estimator that first reduces dimension by principal component analysis and then projects the observations onto the convex hull of the projected latent manifold. We construct a statistical oracle that estimates its supporting hyperplanes from empirical Gaussian tail probabilities of the noisy sample. Under a lower-mass condition on the latent distribution, we prove finite-sample guarantees for the oracle and derive error bounds for the resulting denoiser. The analysis combines risk bounds for least-squares projection under convex constraints with entropy bounds for convex hulls. We also verify the assumptions of the framework for a Cryo-Electron Microscopy observation model by establishing suitable covering number and Lipschitz estimates for the associated group action and imaging operators.
| Comments: | 38 pages, 6 figures |
| Subjects: | Methodology (stat.ME); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.02327 [stat.ME] |
| (or arXiv:2605.02327v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.02327 arXiv-issued DOI via DataCite (pending registration) |
From: Hariharan Narayanan [view email]
[v1]
Mon, 4 May 2026 08:27:53 UTC (3,477 KB)
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