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Life sciences · Preprint
arXiv · September 21, 2026
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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.