One-bit Compressed Sensing using Generative Models

• URL: http://arxiv.org/abs/2502.12762v1
• Date: Tue, 18 Feb 2025 11:28:35 GMT
• Title: One-bit Compressed Sensing using Generative Models
• Authors: Swatantra Kafle, Geethu Joseph, Pramod K. Varshney,
• Abstract summary: This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm. A pre-trained neural network learns to map from a low-dimensional latent space to a higher-dimensional set of sparse vectors. The presented algorithm provides an excellent reconstruction performance because the generative model can learn additional structural information about the signal beyond sparsity.
• Score: 20.819739287436317
• License:
• 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.

Related papers

• Optimality of Approximate Message Passing Algorithms for Spiked Matrix Models with Rotationally Invariant Noise [12.64438771302935]
  We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit.
  arXiv  Detail & Related papers  (2024-05-28T11:42:51Z)
• Compressed Sensing of Generative Sparse-latent (GSL) Signals [9.00058212634219]
  We consider reconstruction of an ambient signal in a compressed sensing (CS) setup where the ambient signal has a neural network based generative model. The ambient signal as generative signal generated a sparse-latent input.
  arXiv  Detail & Related papers  (2023-10-16T12:49:33Z)
• Outlier Detection Using Generative Models with Theoretical Performance Guarantees [11.985270449383272]
  We establish theoretical recovery guarantees for reconstruction of signals using generative models in the presence of outliers. Our results are applicable to both linear generator neural networks and the nonlinear generator neural networks with an arbitrary number of layers.
  arXiv  Detail & Related papers  (2023-10-16T01:25:34Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• Curvature regularization for Non-line-of-sight Imaging from Under-sampled Data [5.591221518341613]
  Non-line-of-sight (NLOS) imaging aims to reconstruct the three-dimensional hidden scenes from the data measured in the line-of-sight. We propose novel NLOS reconstruction models based on curvature regularization. We evaluate the proposed algorithms on both synthetic and real datasets.
  arXiv  Detail & Related papers  (2023-01-01T14:10:43Z)
• A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms [64.3064050603721]
  We generalize Runge-Kutta neural network to a recurrent neural network (R2N2) superstructure for the design of customized iterative algorithms. We demonstrate that regular training of the weight parameters inside the proposed superstructure on input/output data of various computational problem classes yields similar iterations to Krylov solvers for linear equation systems, Newton-Krylov solvers for nonlinear equation systems, and Runge-Kutta solvers for ordinary differential equations.
  arXiv  Detail & Related papers  (2022-11-22T16:30:33Z)
• WNet: A data-driven dual-domain denoising model for sparse-view computed tomography with a trainable reconstruction layer [3.832032989515628]
  We propose WNet, a data-driven dual-domain denoising model which contains a trainable reconstruction layer for sparse-view artifact denoising. We train and test our network on two clinically relevant datasets and we compare the obtained results with three different types of sparse-view CT denoising and reconstruction algorithms.
  arXiv  Detail & Related papers  (2022-07-01T13:17:01Z)
• Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover [87.28082715343896]
  We consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. We design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. The proposed REST network is shown to outperform state-of-the-art model-based and data-driven algorithms in both compressive sensing and radar imaging problems.
  arXiv  Detail & Related papers  (2021-10-20T06:15:45Z)
• Learned Block Iterative Shrinkage Thresholding Algorithm for Photothermal Super Resolution Imaging [52.42007686600479]
  We propose a learned block-sparse optimization approach using an iterative algorithm unfolded into a deep neural network. We show the benefits of using a learned block iterative shrinkage thresholding algorithm that is able to learn the choice of regularization parameters.
  arXiv  Detail & Related papers  (2020-12-07T09:27:16Z)
• Nearly Linear Row Sampling Algorithm for Quantile Regression [54.75919082407094]
  We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data. Based upon our row sampling algorithm, we give the fastest known algorithm for quantile regression and a graph sparsification algorithm for balanced directed graphs.
  arXiv  Detail & Related papers  (2020-06-15T13:40:07Z)
• Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors [52.06292503723978]
  Motivated by advances in compressive sensing with generative models, we study the problem of 1-bit compressive sensing with generative models. We first consider noiseless 1-bit measurements, and provide sample complexity bounds for approximate recovery under i.i.d.Gaussian measurements. We demonstrate that the Binary $epsilon$-Stable Embedding property, which characterizes the robustness of the reconstruction to measurement errors and noise, also holds for 1-bit compressive sensing with Lipschitz continuous generative models.
  arXiv  Detail & Related papers  (2020-02-05T09:44:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.