Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors

2021/08/08 by Zhaoqiang Liu, Subhroshekhar Ghosh, Liu, Zhaoqiang +5 · 2 citations
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2108.03570

openalex publication_date 2021/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1-bit compressive sensing, each measurement is quantized to a single bit, namely the sign of a linear function of an unknown vector, and the goal is to accurately recover the vector. While it is most popular to assume a standard Gaussian sensing matrix for 1-bit compressive sensing, using structured sensing matrices such as partial Gaussian circulant matrices is of significant practical importance due to their faster matrix operations. In this paper, we provide recovery guarantees for a correlation-based optimization algorithm for robust 1-bit compressive sensing with randomly signed partial Gaussian circulant matrices and generative models. Under suitable assumptions, we match guarantees that were previously only known to hold for i.i.d.~Gaussian matrices that require significantly more computation. We make use of a practical iterative algorithm, and perform numerical experiments on image datasets to corroborate our theoretical results.

Citations

• Gradient-based learning applied to document recognition
• Compressed Sensing using Generative Models
• Compressed Sensing with Deep Image Prior and Learned Regularization
• Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors

Cited by

• Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models
• Learning Single Index Models with Diffusion Priors

Related

• One-bit compressed sensing with partial Gaussian circulant matrices
• Robust one-bit compressed sensing with partial circulant matrices
• Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors
• Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
• Guaranteed sparse signal recovery with highly coherent sensing matrices