2022/06/28 by Anna Kuzina, Kumar Pratik, Kuzina, Anna +5 · 1 citation
Computer Science · Earth and Planetary Sciences · Engineering · #FOS: Computer and information sciences #FOS: Electrical engineering #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Underwater Acoustics Research #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2206.14069
openalex publication_date 2022/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.