Abstract
Robust tensor completion recovers multidimensional data from partial observations corrupted by sparse gross errors. Existing convolutional low-rank models typically construct translated copies using circular continuation, which introduces artificial wrap-around neighborhoods for finite nonperiodic data. We propose reflective convolution nuclear norm minimization (RCNNM), which replaces circular shifts with endpoint-nonrepeating reflection. The resulting lifting has nonuniform entry multiplicities and satisfies a weighted Gram identity that supports both the recovery analysis and the optimization method. Under random sampling and sparse corruption, we establish high-probability exact recovery of the underlying tensor and sparse errors, together with stability under bounded dense perturbations. We further develop a two-block ADMM with a closed-form entrywise tensor update, while singular-value thresholding is implemented through the smaller right Gram matrix. Experiments on synthetic tensors, BSDS color images, and CAVE multispectral images show that RCNNM consistently improves over its circular-lifting counterpart, with the clearest gains near image boundaries. In particular, average boundary-PSNR improvements reach 3.26 dB while global reconstruction quality remains competitive.
Keywords
Publication details
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Cite this article
APA 7
Zhou, W., Zhang, F., Qin, W., & Huang, J. (2026). Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization. https://omanscience.com/en/articles/robust-tensor-completion-via-reflective-convolution-nuclear-norm-minimization
MLA 9
Zhou, Weiguo, et al. "Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization." https://omanscience.com/en/articles/robust-tensor-completion-via-reflective-convolution-nuclear-norm-minimization.
Chicago (author–date)
Zhou, Weiguo, Feng Zhang, Wenjin Qin, and Jianwen Huang. 2026. "Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization." https://omanscience.com/en/articles/robust-tensor-completion-via-reflective-convolution-nuclear-norm-minimization.
Harvard
Zhou, W., Zhang, F., Qin, W. and Huang, J. (2026) 'Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization', Available at: https://omanscience.com/en/articles/robust-tensor-completion-via-reflective-convolution-nuclear-norm-minimization.
Vancouver
Zhou W, Zhang F, Qin W, Huang J. Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization. https://omanscience.com/en/articles/robust-tensor-completion-via-reflective-convolution-nuclear-norm-minimization
IEEE
W. Zhou, F. Zhang, W. Qin, and J. Huang, "Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization," https://omanscience.com/en/articles/robust-tensor-completion-via-reflective-convolution-nuclear-norm-minimization.