An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees

• URL: http://arxiv.org/abs/2306.06378v1
• Date: Sat, 10 Jun 2023 08:25:16 GMT
• Title: An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees
• Authors: Alexandros Gkillas, Dimitris Ampeliotis, Kostas Berberidis
• Abstract summary: We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
• Score: 71.57324258813675
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we propose a novel methodology for addressing the hyperspectral image deconvolution problem. This problem is highly ill-posed, and thus, requires proper priors (regularizers) to model the inherent spectral-spatial correlations of the HSI signals. To this end, a new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. To tackle this problem, an effective solver is proposed using the half quadratic splitting methodology. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium (DEQ) framework, resulting in an interpretable architecture, with clear explainability to its parameters and convergence properties with practical benefits. The proposed model is a first attempt to handle the classical HSI degradation problem with different blurring kernels and noise levels via a single deep equilibrium model with significant computational efficiency. Extensive numerical experiments validate the superiority of the proposed methodology over other state-of-the-art methods. This superior restoration performance is achieved while requiring 99.85\% less computation time as compared to existing methods.

Related papers

• Intervening to learn and compose disentangled representations [8.452837716541705]
  We propose a new approach to training arbitrarily expressive generative models that simultaneously learn disentangled latent structure.<n>This is accomplished by adding a simple decoder-only module to the head of an existing decoder block that can be arbitrarily complex.<n>Inspired by the notion of intervention in causal graphical models, our module selectively modifies its architecture during training, allowing it to learn a compact joint model over different contexts.
  arXiv  Detail & Related papers  (2025-07-07T08:30:27Z)
• Structural Similarity-Inspired Unfolding for Lightweight Image Super-Resolution [88.20464308588889]
  We propose a Structural Similarity-Inspired Unfolding (SSIU) method for efficient image SR.<n>This method is designed through unfolding an SR optimization function constrained by structural similarity.<n>Our model outperforms current state-of-the-art models, boasting lower parameter counts and reduced memory consumption.
  arXiv  Detail & Related papers  (2025-06-13T14:29:40Z)
• DiMoSR: Feature Modulation via Multi-Branch Dilated Convolutions for Efficient Image Super-Resolution [7.714092783675679]
  This paper introduces DiMoSR, a novel architecture that enhances feature representation through modulation to complement attention in lightweight SISR networks.<n> Experimental results demonstrate that DiMoSR outperforms state-of-the-art lightweight methods across diverse benchmark datasets.
  arXiv  Detail & Related papers  (2025-05-27T14:40:05Z)
• InvFussion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems [76.39776789410088]
  This work introduces a framework that combines the strong performance of supervised approaches and the flexibility of zero-shot methods.<n>A novel architectural design seamlessly integrates the degradation operator directly into the denoiser.<n> Experimental results on the FFHQ and ImageNet datasets demonstrate state-of-the-art posterior-sampling performance.
  arXiv  Detail & Related papers  (2025-04-02T12:40:57Z)
• A Primal-dual algorithm for image reconstruction with ICNNs [3.4797100095791706]
  We address the optimization problem in a data-driven variational framework, where the regularizer is parameterized by an input- neural network (ICNN) While gradient-based methods are commonly used to solve such problems, they struggle to effectively handle nonsmoothness. We show that a proposed approach outperforms subgradient methods in terms of both speed and stability.
  arXiv  Detail & Related papers  (2024-10-16T10:36:29Z)
• FEM-based Neural Networks for Solving Incompressible Fluid Flows and Related Inverse Problems [41.94295877935867]
  numerical simulation and optimization of technical systems described by partial differential equations is expensive. A comparatively new approach in this context is to combine the good approximation properties of neural networks with the classical finite element method. In this paper, we extend this approach to saddle-point and non-linear fluid dynamics problems, respectively.
  arXiv  Detail & Related papers  (2024-09-06T07:17:01Z)
• CONDA: Condensed Deep Association Learning for Co-Salient Object Detection [136.30039346735833]
  This paper proposes a deep association learning strategy that deploys deep networks on raw associations to transform them into deep association features. Experimental results in three benchmark datasets demonstrate the remarkable effectiveness of our proposed method with various training settings.
  arXiv  Detail & Related papers  (2024-09-02T08:01:32Z)
• Alternating Minimization Schemes for Computing Rate-Distortion-Perception Functions with $f$-Divergence Perception Constraints [10.564071872770146]
  We study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources. We characterize the optimal parametric solutions. We provide sufficient conditions on the distortion and the perception constraints.
  arXiv  Detail & Related papers  (2024-08-27T12:50:12Z)
• The Stochastic Conjugate Subgradient Algorithm For Kernel Support Vector Machines [1.738375118265695]
  This paper proposes an innovative method specifically designed for kernel support vector machines (SVMs) It not only achieves faster iteration per iteration but also exhibits enhanced convergence when compared to conventional SFO techniques. Our experimental results demonstrate that the proposed algorithm not only maintains but potentially exceeds the scalability of SFO methods.
  arXiv  Detail & Related papers  (2024-07-30T17:03:19Z)
• Robust Latent Representation Tuning for Image-text Classification [9.789498730131607]
  We propose a robust latent representation tuning method for large models. Our approach introduces a modality latent translation module to maximize the correlation between modalities, resulting in a robust representation. Within this framework, common semantics are refined during training, and robust performance is achieved even in the absence of one modality.
  arXiv  Detail & Related papers  (2024-06-10T06:29:00Z)
• Adaptive Federated Learning Over the Air [108.62635460744109]
  We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. Our analysis shows that the AdaGrad-based training algorithm converges to a stationary point at the rate of $mathcalO( ln(T) / T 1 - frac1alpha ).
  arXiv  Detail & Related papers  (2024-03-11T09:10:37Z)
• Enhancing Low-Order Discontinuous Galerkin Methods with Neural Ordinary Differential Equations for Compressible Navier--Stokes Equations [0.1578515540930834]
  We introduce an end-to-end differentiable framework for solving the compressible Navier-Stokes equations. This integrated approach combines a differentiable discontinuous Galerkin solver with a neural network source term. We demonstrate the performance of the proposed framework through two examples.
  arXiv  Detail & Related papers  (2023-10-29T04:26:23Z)
• Adaptive operator learning for infinite-dimensional Bayesian inverse problems [7.716833952167609]
  We develop an adaptive operator learning framework that can reduce modeling error gradually by forcing the surrogate to be accurate in local areas. We present a rigorous convergence guarantee in the linear case using the UKI framework. The numerical results show that our method can significantly reduce computational costs while maintaining inversion accuracy.
  arXiv  Detail & Related papers  (2023-10-27T01:50:33Z)
• Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixing [16.02193274044797]
  We propose a new interpretable deep learning method for hyperspectral unmixing that accounts for nonlinearity and endmember variability. The model is learned end-to-end using backpropagation, and trained using a self-supervised strategy. Experimental results on synthetic and real datasets illustrate the performance of the proposed method.
  arXiv  Detail & Related papers  (2023-10-03T18:21:37Z)
• Revisiting Context Aggregation for Image Matting [57.90127743270313]
  We present AEMatter, a matting network that is straightforward yet very effective. AEMatter adopts a Hybrid-Transformer backbone with appearance-enhanced axis-wise learning (AEAL) blocks to build a basic network with strong context aggregation learning capability. Extensive experiments on five popular matting datasets demonstrate that the proposed AEMatter outperforms state-of-the-art matting methods by a large margin.
  arXiv  Detail & Related papers  (2023-04-03T17:40:30Z)
• On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
  We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
  arXiv  Detail & Related papers  (2023-02-05T01:39:21Z)
• Exploring the Algorithm-Dependent Generalization of AUPRC Optimization with List Stability [107.65337427333064]
  optimization of the Area Under the Precision-Recall Curve (AUPRC) is a crucial problem for machine learning. In this work, we present the first trial in the single-dependent generalization of AUPRC optimization. Experiments on three image retrieval datasets on speak to the effectiveness and soundness of our framework.
  arXiv  Detail & Related papers  (2022-09-27T09:06:37Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Deep Variational Network Toward Blind Image Restoration [60.45350399661175]
  Blind image restoration is a common yet challenging problem in computer vision. We propose a novel blind image restoration method, aiming to integrate both the advantages of them. Experiments on two typical blind IR tasks, namely image denoising and super-resolution, demonstrate that the proposed method achieves superior performance over current state-of-the-arts.
  arXiv  Detail & Related papers  (2020-08-25T03:30:53Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Multi-Scale Boosted Dehazing Network with Dense Feature Fusion [92.92572594942071]
  We propose a Multi-Scale Boosted Dehazing Network with Dense Feature Fusion based on the U-Net architecture. We show that the proposed model performs favorably against the state-of-the-art approaches on the benchmark datasets as well as real-world hazy images.
  arXiv  Detail & Related papers  (2020-04-28T09:34:47Z)

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.