Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction

TL;DR

This paper introduces a federated tensor decomposition method for multimodal image reconstruction that improves quality and reduces communication costs by leveraging low-rank Tucker decomposition with personalized ranks.

Contribution

It proposes a novel federated low-rank tensor estimation technique using Tucker decomposition with randomized sketching, supporting heterogeneous ranks and efficient communication.

Findings

Achieves higher reconstruction quality than existing methods.

Reduces communication costs through tensor sketching.

Supports personalized tensor ranks for clients.

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.