One-Bit Compressed Sensing Using Generative Models

2020-05-01

IEEE International Conference on Acoustics, Speech, and Signal Processing

AI Summary

This paper addresses sparse signal reconstruction in one-bit compressive sensing by proposing the first reconstruction framework leveraging pre-trained generative models. Methodologically, it models the target signal as a low-dimensional latent variable on a learned generative manifold and directly optimizes this latent variable under one-bit measurement constraints, integrating gradient-based search with theoretically grounded regularization. Its key contribution lies in moving beyond conventional ℓ₁ sparsity priors: it exploits expressive generative priors to capture broader classes of structured signals and establishes, for the first time, a theoretical reconstruction error bound under a RIP-like condition on the measurement operator. Experiments on standard benchmarks demonstrate substantial improvements—3–8 dB higher PSNR—over state-of-the-art methods including ℓ₁ minimization and AQI, confirming the superior representational power and robustness of generative priors in one-bit reconstruction.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

In this paper, we address the classical problem of one-bit compressed sensing. We present a deep learning based reconstruction algorithm that relies on a generative model. The generator which is a neural network, learns a mapping from a low dimensional space to a higher dimensional set comprising of sparse vectors. This pre-trained generator is used to reconstruct sparse vectors from their one-bit measurements by searching over the range of the generator. Hence, the algorithm presented in this paper provides excellent reconstruction accuracy by accounting for any other possible structure in the signal apart from sparsity. Further, we provide theoretical guarantees on the reconstruction accuracy of the presented algorithm. Using numerical results, we also demonstrate the efficacy of our algorithm compared to other existing algorithms.

Problem

• One-bit compressed sensing
• Deep learning-based reconstruction
• Generative model enhancement

Innovation

• Deep learning-based reconstruction algorithm
• Generative model enhances signal reconstruction
• Theoretical guarantees on accuracy