<ul data-eligibleForWebStory="true"><li>Existing tensor recovery methods do not consider the impact of tensor scale variations on structural characteristics.</li><li>Current studies face computational challenges when dealing with large-scale high-order tensor data.</li><li>New algorithms leveraging Krylov subspace iteration, block Lanczos bidiagonalization process, and random projection strategies are introduced for low-rank tensor approximation.</li><li>The algorithms establish theoretical bounds on the accuracy of the approximation error estimate.</li><li>A novel nonconvex modeling framework is created for large-scale tensor recovery, utilizing a new regularization paradigm for insightful prior representation.</li><li>Unified nonconvex models and optimization algorithms are developed for various high-order tensor recovery tasks in unquantized and quantized scenarios.</li><li>Randomized LRTA schemes are integrated into computations to make the proposed algorithms practical and efficient for large-scale tensor data.</li><li>Extensive experiments on large-scale tensors show the effectiveness and superiority of the proposed method over state-of-the-art approaches.</li></ul>

Accelerating Large-Scale Regularized High-Order Tensor Recovery

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