# Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction

arXiv: https://arxiv.org/abs/2502.02761 · HTML: https://mlsanity.com/paper/2502.02761/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [FDLoRA: Personalized Federated Learning of Large Language Model via Dual LoRA Tuning](https://mlsanity.com/paper/2406.07925/) (2024)
- [Federated Learning via Decentralized Dataset Distillation in Resource-Constrained Edge Environments](https://mlsanity.com/paper/2208.11311/) (2022)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [FEDZIP: A Compression Framework for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2102.01593/) (2021)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography](https://mlsanity.com/paper/1307.5348/) (2013)
- [Hypernetwork-based Personalized Federated Learning for Multi-Institutional CT Imaging](https://mlsanity.com/paper/2206.03709/) (2022)
- [Tensor Regression Using Low-rank and Sparse Tucker Decompositions](https://mlsanity.com/paper/1911.03725/) (2019)
- [Decomposition of Big Tensors With Low Multilinear Rank](https://mlsanity.com/paper/1412.1885/) (2014)
- [Communication-Efficient Federated Low-Rank Update Algorithm and its Connection to Implicit Regularization](https://mlsanity.com/paper/2409.12371/) (2024)
- [Federated Learning Using Coupled Tensor Train Decomposition](https://mlsanity.com/paper/2403.02898/) (2024)
- [FCNCP: A Coupled Nonnegative CANDECOMP/PARAFAC Decomposition Based on Federated Learning](https://mlsanity.com/paper/2404.11890/) (2024)
- [FIRM: Federated Image Reconstruction using Multimodal Tomographic Data](https://mlsanity.com/paper/2501.05642/) (2025)

## Abstract (arXiv)

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.