联邦学习中用张量分解实现多模态图像重建，提升效果与通信效率
Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction
- 采用塔克分解与随机投影，避免全尺寸张量重建
- 相比现有方法，重建质量更高且通信量减少
- 支持异构客户端自适应选择分解阶数，适合资源受限场景
低秩张量估计为应对高维数据挑战提供了有效手段，可显著改善在噪声或欠采样条件下的图像重建等不适定逆问题。同时，张量分解因其能挖掘潜在空间结构并提升通信效率，在联邦学习中备受关注。本文提出一种基于塔克分解的联邦图像重建方法，结合联合因子分解与随机投影技术，以处理大规模多模态数据。该方法无需重建完整张量，支持异构秩设置，使各客户端可根据先验知识或通信能力自主选择分解阶数。数值实验表明，该方法在重建质量与通信压缩方面均优于现有方法，展现出在联邦学习环境下解决多模态逆问题的巨大潜力。
原文摘要 · Abstract (English)
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.
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