One-bit Compressed Sensing using Generative Models

--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. Index terms-- Sparsity, one-bit compressed sensing, Lips-chitz continuous generative models, variational autoencoders, image compression I. Over the past two decades, research in compressed sensing (CS) [2], [3] has expanded rapidly, leading to advancements in signal reconstruction algorithms [4]-[8] and inference tasks such as detection, estimation, and classification [9]-[12]. The success of CS, coupled with the fundamental role of quantization in signal digitization, has fueled a growing interest in quantized CS [13]-[15]. Coarse quantization is particularly appealing as it results in significant reduction in bandwidth requirements and power consumption. One of the more popular quantization schemes is one-bit quantization, wherein the measurements are binarized by comparing signals/measurements to a fixed reference level. Using the zero reference level is the most used one-bit quantization scheme, which is also the focus of our paper. Here, the measurements are quantized based on their signs. The popularity of one-bit quantization stems from its simplicity, cost-effectiveness, and robustness to certain linear and nonlinear distortions, such as saturation [16], [17]. The material in this paper was presented in part at the IEEE International Conference on Acoustics, Speech, & Signal Processing (ICASSP), Barcelona, Spain in May 2020 [1].