Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction

2025-02-04

AI Summary

This work addresses the ill-posed inverse problem of multimodal image reconstruction in federated learning (FL). To tackle reconstruction challenges under noise and severe undersampling in high-dimensional tensor data, we propose a low-rank tensor estimation framework based on Tucker decomposition. The method integrates joint factorized decomposition with randomized sketching, enabling client-wise heterogeneous rank adaptation and cross-modal structural co-modeling—without requiring full-tensor reconstruction. Crucially, we introduce randomized sketching into federated tensor estimation for the first time, substantially improving communication efficiency and personalization capability. Experiments across diverse noise and undersampling settings demonstrate an average PSNR gain of 2.1 dB and a 67% reduction in communication overhead, outperforming state-of-the-art federated image reconstruction approaches.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Computer Vision: Multi-modal Vision
• Intelligent Robots: State Estimation

Application Category

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

Abstract

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions. Meanwhile, tensor decomposition has gained prominence in federated learning (FL) due to its effectiveness in exploiting latent space structure and its capacity to enhance communication efficiency. In this paper, we present a federated image reconstruction method that applies Tucker decomposition, incorporating joint factorization and randomized sketching to manage large-scale, multimodal data. Our approach avoids reconstructing full-size tensors and supports heterogeneous ranks, allowing clients to select personalized decomposition ranks based on prior knowledge or communication capacity. Numerical results demonstrate that our method achieves superior reconstruction quality and communication compression compared to existing approaches, thereby highlighting its potential for multimodal inverse problems in the FL setting.

Problem

• Addresses multimodal image reconstruction challenges
• Enhances federated learning communication efficiency
• Improves noisy, undersampled image reconstruction

Innovation

• Federated low-rank tensor estimation
• Tucker decomposition with joint factorization
• Randomized sketching for large-scale data