One-bit Compressed Sensing using Generative Models

TL;DR

This paper introduces a deep learning-based method for one-bit compressed sensing that uses a pre-trained generative model to improve signal reconstruction accuracy, supported by theoretical guarantees and empirical results.

Contribution

It proposes a novel reconstruction algorithm leveraging generative models for one-bit compressed sensing, with theoretical analysis and superior empirical performance.

Findings

Achieves high reconstruction accuracy from one-bit measurements.

Provides theoretical guarantees on reconstruction and sample complexity.

Outperforms existing algorithms on image datasets.

Abstract

This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a pre-trained neural network, learns to map from a low-dimensional latent space to a higher-dimensional set of sparse vectors. This generator is then used to reconstruct sparse vectors from their one-bit measurements by searching over its range. The presented algorithm provides an excellent reconstruction performance because the generative model can learn additional structural information about the signal beyond sparsity. Furthermore, we provide theoretical guarantees on the reconstruction accuracy and sample complexity of the algorithm. Through numerical experiments using three publicly available image datasets, MNIST, Fashion-MNIST, and Omniglot, we demonstrate the superior performance of the algorithm compared to other existing algorithms and show that our algorithm can recover both the amplitude and the direction of the signal from one-bit measurements.