Guaranteed Low-Rank Tensor Recovery from Modewise Measurements via Normalized Block-Weighted Riemannian Gradient Descent

2026-09-21

AI Summary

本文提出了一种基于模态加权黎曼梯度下降的方法，用于从线性测量中恢复低秩张量，改进了收敛速度和计算效率。

Abstract

We consider the recovery of low-multilinear-rank tensors from linear measurements and propose an adaptive block-weighted modewise Riemannian gradient descent method. The method combines memory-efficient modewise measurements with a normalized adaptive weighting strategy for the core and factor components of the Riemannian gradient. The weighting improves convergence without increasing the multilinear-rank bound of the search direction or the size of the reduced core used for retraction. Under the tensor restricted isometry property and a suitable initialization, we establish local linear convergence and derive sampling guarantees for sub-Gaussian and subsampled orthogonal with random sign (SORS) measurements. Numerical experiments on synthetic low-Tucker-rank tensors show that the proposed method reduces iteration counts and computational time while maintaining reliable recovery performance, especially near the recovery threshold and for structured SORS measurements.

Problem

• low-multilinear-rank tensors
• linear measurements
• tensor recovery
• Riemannian gradient descent
• modewise measurements

Innovation

• adaptive block-weighted modewise Riemannian gradient descent
• low-multilinear-rank tensor recovery
• normalized adaptive weighting
• tensor restricted isometry property
• sub-Gaussian and SORS measurements