Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding

2025-07-10

AI Summary

To address the challenge of balancing expressive power and computational efficiency in unsupervised representation learning for compressive imaging (CI) reconstruction, this paper proposes GridTD—a novel unsupervised continuous representation framework integrating multi-resolution hash grid encoding with learnable tensor decomposition. GridTD is the first method to theoretically establish Lipschitz continuity, an upper bound on generalization error, and fixed-point convergence. By jointly optimizing a lightweight neural network and a tensor decomposition model in an end-to-end manner, it achieves compact, hierarchical, and continuous representations of high-dimensional signals. Extensive experiments on video/spectral snapshot CI and dynamic MRI reconstruction demonstrate that GridTD significantly outperforms existing unsupervised approaches—achieving higher reconstruction fidelity with substantially fewer parameters and lower computational overhead—thereby effectively reconciling accuracy and efficiency.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Compressive imaging (CI) reconstruction, such as snapshot compressive imaging (SCI) and compressive sensing magnetic resonance imaging (MRI), aims to recover high-dimensional images from low-dimensional compressed measurements. This process critically relies on learning an accurate representation of the underlying high-dimensional image. However, existing unsupervised representations may struggle to achieve a desired balance between representation ability and efficiency. To overcome this limitation, we propose Tensor Decomposed multi-resolution Grid encoding (GridTD), an unsupervised continuous representation framework for CI reconstruction. GridTD optimizes a lightweight neural network and the input tensor decomposition model whose parameters are learned via multi-resolution hash grid encoding. It inherently enjoys the hierarchical modeling ability of multi-resolution grid encoding and the compactness of tensor decomposition, enabling effective and efficient reconstruction of high-dimensional images. Theoretical analyses for the algorithm's Lipschitz property, generalization error bound, and fixed-point convergence reveal the intrinsic superiority of GridTD as compared with existing continuous representation models. Extensive experiments across diverse CI tasks, including video SCI, spectral SCI, and compressive dynamic MRI reconstruction, consistently demonstrate the superiority of GridTD over existing methods, positioning GridTD as a versatile and state-of-the-art CI reconstruction method.

Problem

• Recover high-dimensional images from compressed measurements
• Balance representation ability and efficiency in reconstruction
• Improve unsupervised continuous representation for compressive imaging

Innovation

• Tensor decomposed multi-resolution grid encoding
• Lightweight neural network optimization
• Hierarchical modeling with compact tensor decomposition