# Fast Compressive Sensing Recovery Using Generative Models with Structured Latent Variables

## TL;DR

This paper introduces a fast compressive sensing recovery method leveraging structured latent variables in generative models, improving accuracy and stability with limited measurements while maintaining realistic image features.

## Contribution

It proposes a novel algorithm that constrains latent variables for stable, high-quality image reconstruction from few measurements using structured generative models.

## Key findings

- Enhanced reconstruction accuracy with limited measurements
- Preserves realistic and non-smooth image features
- Achieves high computational speed through alternating projections

## Abstract

Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a generative model. We search and constrain on latent variable space to make the method stable when the number of compressed measurements is extremely limited. We show that, by exploiting certain structures of the latent variables, the proposed method produces improved reconstruction accuracy and preserves realistic and non-smooth features in the image. Our algorithm achieves high computation speed by projecting between the original signal space and the latent variable space in an alternating fashion.