Learning Spatially Adaptive $\ell_1$-Norms Weights for Convolutional Synthesis Regularization

• URL: http://arxiv.org/abs/2503.09483v2
• Date: Mon, 17 Mar 2025 10:38:39 GMT
• Title: Learning Spatially Adaptive $\ell_1$-Norms Weights for Convolutional Synthesis Regularization
• Authors: Andreas Kofler, Luca Calatroni, Christoph Kolbitsch, Kostas Papafitsoros,
• Abstract summary: We consider a family of pre-trained convolutional filters and estimate deeply parametrized spatially varying parameters applied to sparse feature maps.<n>We show that the proposed approach produces visually and quantitatively comparable results with the latter approaches and at the same time remains highly interpretable.
• Score: 1.1699566743796068
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an unrolled algorithm approach for learning spatially adaptive parameter maps in the framework of convolutional synthesis-based $\ell_1$ regularization. More precisely, we consider a family of pre-trained convolutional filters and estimate deeply parametrized spatially varying parameters applied to the sparse feature maps by means of unrolling a FISTA algorithm to solve the underlying sparse estimation problem. The proposed approach is evaluated for image reconstruction of low-field MRI and compared to spatially adaptive and non-adaptive analysis-type procedures relying on Total Variation regularization and to a well-established model-based deep learning approach. We show that the proposed approach produces visually and quantitatively comparable results with the latter approaches and at the same time remains highly interpretable. In particular, the inferred parameter maps quantify the local contribution of each filter in the reconstruction, which provides valuable insight into the algorithm mechanism and could potentially be used to discard unsuited filters.

Related papers

• A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters [15.640261000544077]
  We present a new perspective on the origin and interpretation of adaptive filters.<n>We can present, in a unified framework, derivations of many adaptive filters which depend on the probabilistic model of the observational noise.<n> Numerical examples are shown to illustrate the properties and provide a better insight into the performance of the derived adaptive filters.
  arXiv  Detail & Related papers  (2025-02-25T16:20:10Z)
• Truncating Trajectories in Monte Carlo Policy Evaluation: an Adaptive Approach [51.76826149868971]
  Policy evaluation via Monte Carlo simulation is at the core of many MC Reinforcement Learning (RL) algorithms. We propose as a quality index a surrogate of the mean squared error of a return estimator that uses trajectories of different lengths. We present an adaptive algorithm called Robust and Iterative Data collection strategy Optimization (RIDO)
  arXiv  Detail & Related papers  (2024-10-17T11:47:56Z)
• Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanism [0.4604003661048266]
  We propose AdOBEst-LDP, a new algorithm for adaptive, online Bayesian estimation of categorical distributions under local differential privacy.<n>By adapting the subset selection process to the past privatized data via Bayesian estimation, the algorithm improves the utility of future privatized data.
  arXiv  Detail & Related papers  (2024-05-11T13:59:52Z)
• Closed-form Filtering for Non-linear Systems [83.91296397912218]
  We propose a new class of filters based on Gaussian PSD Models, which offer several advantages in terms of density approximation and computational efficiency. We show that filtering can be efficiently performed in closed form when transitions and observations are Gaussian PSD Models. Our proposed estimator enjoys strong theoretical guarantees, with estimation error that depends on the quality of the approximation and is adaptive to the regularity of the transition probabilities.
  arXiv  Detail & Related papers  (2024-02-15T08:51:49Z)
• 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)
• Joint State Estimation and Noise Identification Based on Variational Optimization [8.536356569523127]
  A novel adaptive Kalman filter method based on conjugate-computation variational inference, referred to as CVIAKF, is proposed. The effectiveness of CVIAKF is validated through synthetic and real-world datasets of maneuvering target tracking.
  arXiv  Detail & Related papers  (2023-12-15T07:47:03Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Adaptive Stochastic Optimisation of Nonconvex Composite Objectives [2.1700203922407493]
  We propose and analyse a family of generalised composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. We exploit the low-dimensional structure of the decision sets for high-dimensional problems.
  arXiv  Detail & Related papers  (2022-11-21T18:31:43Z)
• Adaptive Zeroth-Order Optimisation of Nonconvex Composite Objectives [1.7640556247739623]
  We analyze algorithms for zeroth-order entropy composite objectives, focusing on dependence on dimensionality. This is achieved by exploiting low dimensional structure of the decision set using the mirror descent method with an estimation alike function. To improve the gradient, we replace the classic sampling method based on Rademacher and show that the mini-batch method copes with non-Eucli geometry.
  arXiv  Detail & Related papers  (2022-08-09T07:36:25Z)
• Study of Proximal Normalized Subband Adaptive Algorithm for Acoustic Echo Cancellation [23.889870461547105]
  We propose a novel normalized subband adaptive filter algorithm suited for sparse scenarios. The proposed algorithm is derived based on the proximal forward-backward splitting and the soft-thresholding methods. We analyze the mean and mean square behaviors of the algorithm, which is supported by simulations.
  arXiv  Detail & Related papers  (2021-08-14T22:20:09Z)
• Harnessing Heterogeneity: Learning from Decomposed Feedback in Bayesian Modeling [68.69431580852535]
  We introduce a novel GP regression to incorporate the subgroup feedback. Our modified regression has provably lower variance -- and thus a more accurate posterior -- compared to previous approaches. We execute our algorithm on two disparate social problems.
  arXiv  Detail & Related papers  (2021-07-07T03:57:22Z)
• An AI-Assisted Design Method for Topology Optimization Without Pre-Optimized Training Data [68.8204255655161]
  An AI-assisted design method based on topology optimization is presented, which is able to obtain optimized designs in a direct way. Designs are provided by an artificial neural network, the predictor, on the basis of boundary conditions and degree of filling as input data.
  arXiv  Detail & Related papers  (2020-12-11T14:33:27Z)
• Stochastic batch size for adaptive regularization in deep network optimization [63.68104397173262]
  We propose a first-order optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework. We empirically demonstrate the effectiveness of our algorithm using an image classification task based on conventional network models applied to commonly used benchmark datasets.
  arXiv  Detail & Related papers  (2020-04-14T07:54:53Z)

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.