2019/06/05 by Feng Zhang, Zhang, Feng, Wendong Wang +7 · 1 citation
Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1906.01774
openalex publication_date 2019/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The essential task of tensor data analysis focuses on the tensor decomposition and the corresponding notion of rank. In this paper, by introducing the notion of tensor Singular Value Decomposition (t-SVD), we establish a Regularized Tensor Nuclear Norm Minimization (RTNNM) model for low-tubal-rank tensor recovery. As we know that many variants of the Restricted Isometry Property (RIP) have proven to be crucial analysis tools for sparse recovery. In the t-SVD framework, we initiatively define a novel tensor Restricted Isometry Property (t-RIP). Furthermore, we show that any third-order tensor \boldsymbolX can stably be recovered from few linear noise measurements under some certain t-RIP conditions via the RTNNM model. We note that, as far as the authors are aware, such kind of result has not previously been reported in the literature.