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Efficient and compact tensor wheel decomposition for tensor completion
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AI
DOI：10.1016/j.patcog.2025.112377.png)
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Abstract
En 中文
Tensor wheel (TW) decomposition has recently emerged as a powerful technique for achieving state-of-the-art recovery performance in tensor completion tasks. However, its widespread application has been hindered by issues related to rank sensitivity and high computational cost. To address these limitations, we introduce an efficient and compact TW decomposition method for low-rank tensor completion. Specifically, we demonstrate that the model complexity of TW decomposition is controlled simultaneously by two elements, namely, the explicit TW rank and implicit sparsity in the core tensor. Therefore, low-rank and sparsity regularization are introduced to ring factors and core factor, respectively, to achieve a compact TW decomposition. Furthermore, to alleviate the computational bottleneck of TW decomposition, we propose a novel generalized inverse operation, which reduces the computational complexity of vanilla TW decomposition from O(INR2N) to O(INRN). Subsequently, we develop an efficient alternating direction method of multipliers (ADMM) algorithm with theoretical convergence guarantees. Numerical tensor completion experiments on color images, multispectral images, and color videos demonstrate that the proposed method achieves superior performance while significantly reducing runtime compared to state-of-the-art methods. The code is available at: https://github.com/justicbro/TWLRS .
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