From sparse recovery to plug-and-play priors, understanding trade-offs for stable recovery with generalized projected gradient descent

• URL: http://arxiv.org/abs/2512.07397v1
• Date: Mon, 08 Dec 2025 10:31:48 GMT
• Title: From sparse recovery to plug-and-play priors, understanding trade-offs for stable recovery with generalized projected gradient descent
• Authors: Ali Joundi, Yann Traonmilin, Jean-François Aujol,
• Abstract summary: We consider the problem of recovering an unknown low-dimensional vector from noisy, underdetermined observations.<n>We focus on the Generalized Projected Gradient Descent (GPGD) framework, which unifies traditional sparse recovery methods and modern approaches.
• Score: 2.599882743586164
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of recovering an unknown low-dimensional vector from noisy, underdetermined observations. We focus on the Generalized Projected Gradient Descent (GPGD) framework, which unifies traditional sparse recovery methods and modern approaches using learned deep projective priors. We extend previous convergence results to robustness to model and projection errors. We use these theoretical results to explore ways to better control stability and robustness constants. To reduce recovery errors due to measurement noise, we consider generalized back-projection strategies to adapt GPGD to structured noise, such as sparse outliers. To improve the stability of GPGD, we propose a normalized idempotent regularization for the learning of deep projective priors. We provide numerical experiments in the context of sparse recovery and image inverse problems, highlighting the trade-offs between identifiability and stability that can be achieved with such methods.

Related papers

• Stochastic Orthogonal Regularization for deep projective priors [2.990411348977783]
  In this paper, we focus on generalized projected descent gradient (GPGD) algorithms.<n> neural networks allow for projections onto unknown low-dimensional sets that model complex data, such as images.
  arXiv  Detail & Related papers  (2025-05-19T13:12:01Z)
• PtyGenography: using generative models for regularization of the phase retrieval problem [0.562479170374811]
  We compare the reconstruction properties of classical and generative inverse problem formulations.<n>We propose a new unified reconstruction approach that mitigates overfitting to the generative model for varying noise levels.
  arXiv  Detail & Related papers  (2025-02-03T13:26:55Z)
• Addressing the Inconsistency in Bayesian Deep Learning via Generalized Laplace Approximation [17.224114053715528]
  We introduce the generalized Laplace approximation, which requires only a simple modification to the Hessian calculation of the regularized loss.<n>We evaluate the proposed method on state-of-the-art neural networks and real-world datasets, demonstrating that the generalized Laplace approximation enhances predictive performance.
  arXiv  Detail & Related papers  (2024-05-22T11:11:42Z)
• 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)
• Domain Generalization Guided by Gradient Signal to Noise Ratio of Parameters [69.24377241408851]
  Overfitting to the source domain is a common issue in gradient-based training of deep neural networks. We propose to base the selection on gradient-signal-to-noise ratio (GSNR) of network's parameters.
  arXiv  Detail & Related papers  (2023-10-11T10:21:34Z)
• Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems [8.33626757808923]
  We introduce Convex Latent-d Adrial Regularizers (CLEAR), a novel and interpretable data-driven paradigm. CLEAR represents a fusion of deep learning (DL) and variational regularization. Our method consistently outperforms conventional data-driven techniques and traditional regularization approaches.
  arXiv  Detail & Related papers  (2023-09-17T12:06:04Z)
• DiffusionAD: Norm-guided One-step Denoising Diffusion for Anomaly Detection [80.20339155618612]
  DiffusionAD is a novel anomaly detection pipeline comprising a reconstruction sub-network and a segmentation sub-network.<n>A rapid one-step denoising paradigm achieves hundreds of times acceleration while preserving comparable reconstruction quality.<n>Considering the diversity in the manifestation of anomalies, we propose a norm-guided paradigm to integrate the benefits of multiple noise scales.
  arXiv  Detail & Related papers  (2023-03-15T16:14:06Z)
• A Bayesian Robust Regression Method for Corrupted Data Reconstruction [5.298637115178182]
  We develop an effective robust regression method that can resist adaptive adversarial attacks. First, we propose the novel TRIP (hard Thresholding approach to Robust regression with sImple Prior) algorithm. We then use the idea of Bayesian reweighting to construct the more robust BRHT (robust Bayesian Reweighting regression via Hard Thresholding) algorithm.
  arXiv  Detail & Related papers  (2022-12-24T17:25:53Z)
• Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networks [59.142826407441106]
  We study the generalization behavior of shallow neural networks (SNNs) by leveraging the concept of algorithmic stability. We consider gradient descent (GD) and gradient descent (SGD) to train SNNs, for both of which we develop consistent excess bounds.
  arXiv  Detail & Related papers  (2022-09-19T18:48:00Z)
• 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)
• Benign Overfitting of Constant-Stepsize SGD for Linear Regression [122.70478935214128]
  inductive biases are central in preventing overfitting empirically. This work considers this issue in arguably the most basic setting: constant-stepsize SGD for linear regression. We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares.
  arXiv  Detail & Related papers  (2021-03-23T17:15:53Z)
• On the Convergence Rate of Projected Gradient Descent for a Back-Projection based Objective [58.33065918353532]
  We consider a back-projection based fidelity term as an alternative to the common least squares (LS) We show that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms.
  arXiv  Detail & Related papers  (2020-05-03T00:58:23Z)

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.