Sparse Bayesian Generative Modeling for Compressive Sensing

• URL: http://arxiv.org/abs/2411.09483v1
• Date: Thu, 14 Nov 2024 14:37:47 GMT
• Title: Sparse Bayesian Generative Modeling for Compressive Sensing
• Authors: Benedikt Böck, Sadaf Syed, Wolfgang Utschick,
• Abstract summary: This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.
• Score: 8.666730973498625
• License:
• Abstract: This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.

Related papers

• Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance [52.093434664236014]
  Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. Inspired by this finding, we propose to improve recent methods by using more principled covariance determined by maximum likelihood estimation.
  arXiv  Detail & Related papers  (2024-02-03T13:35:39Z)
• MAST: Model-Agnostic Sparsified Training [4.962431253126472]
  We introduce a novel optimization problem formulation that departs from the conventional way of minimizing machine learning model loss as a black-box function. Unlike traditional formulations, the proposed approach explicitly incorporates an initially pre-trained model and random sketch operators. We present several variants of the Gradient Descent (SGD) method adapted to the new problem formulation.
  arXiv  Detail & Related papers  (2023-11-27T18:56:03Z)
• Approximate Message Passing for the Matrix Tensor Product Model [8.206394018475708]
  We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model. Building upon an convergence theorem for non-separable functions, we prove a state evolution for non-separable functions. We leverage this state evolution result to provide necessary and sufficient conditions for recovery of the signal of interest.
  arXiv  Detail & Related papers  (2023-06-27T16:03:56Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• A Sparsity-promoting Dictionary Model for Variational Autoencoders [16.61511959679188]
  Structuring the latent space in deep generative models is important to yield more expressive models and interpretable representations. We propose a simple yet effective methodology to structure the latent space via a sparsity-promoting dictionary model.
  arXiv  Detail & Related papers  (2022-03-29T17:13:11Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models [47.208080968675574]
  We study the use of generative models in inverse problems with more complete understanding. We support our claims with experimental results for solving various inverse problems. We propose an extension of our approach that can handle model mismatch (i.e., situations where the generative prior is not exactly applicable)
  arXiv  Detail & Related papers  (2021-05-13T15:58:27Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Uncertainty Modelling in Risk-averse Supply Chain Systems Using Multi-objective Pareto Optimization [0.0]
  One of the arduous tasks in supply chain modelling is to build robust models against irregular variations. We have introduced a novel methodology namely, Pareto Optimization to handle uncertainties and bound the entropy of such uncertainties by explicitly modelling them under some apriori assumptions.
  arXiv  Detail & Related papers  (2020-04-24T21:04:25Z)

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.