Denoising data using convex relaxations

arXiv:2605.02327v1 Announce Type: cross 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 (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.

Source: arXiv cs.LG | 2026-05-05