Equivariant Priors for Compressed Sensing with Unknown Orientation

TL;DR

This paper introduces equivariant generative models as priors for compressed sensing, enabling the recovery of signals with unknown orientations through gradient descent and providing theoretical guarantees.

Contribution

It proposes using equivariant variational autoencoders as priors in compressed sensing to handle unknown orientations, with theoretical recovery guarantees.

Findings

Successful recovery of signals with unknown orientations.

Theoretical guarantees for signal reconstruction.

Potential improvements in convergence and latency.

Abstract

In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the signal has an unknown orientation prior to measurements. To address such recovery problems, we propose using equivariant generative models as a prior, which encapsulate orientation information in their latent space. Thereby, we show that signals with unknown orientations can be recovered with iterative gradient descent on the latent space of these models and provide additional theoretical recovery guarantees. We construct an equivariant variational autoencoder and use the decoder as generative prior for compressed sensing. We discuss additional potential gains of the proposed approach in terms of convergence and latency.