# Denoising data using convex relaxations

arXiv: https://arxiv.org/abs/2605.02327 · HTML: https://mlsanity.com/paper/2605.02327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 17 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 1 of 1)

- [Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions](https://mlsanity.com/paper/1501.07242/) (2015)

## Abstract (arXiv)

We study the problem of denoising observations (Yi=Xi+Zi), where the latent variables (Xi) are sampled from a low-dimensional manifold in (ℝn) and the noise variables (Zi) 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.