Journal ArticleDeepTensor: Low-Rank Tensor Decomposition With Deep Network PriorsSaragadam, Vishwanath; Balestriero, Randall; Veeraraghavan, Ashok; Baraniuk, Richard GDeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors where each low-rank tensor is generated by a deep network (DN) that is trained in a self-supervised manner to minimize the mean-square approximation error. Our key observation is that the implicit regularization inherent in DNs enables them to capture nonlinear signal structures that are out of the reach of classical linear methods like the singular value decomposition (SVD) and principal components analysis (PCA). We demonstrate that the performance of DeepTensor is robust to a wide range of distributions and a computationally efficient drop-in replacement for the SVD, PCA, nonnegative matrix factorization (NMF), and similar decompositions by exploring a range of real-world applications, including hyperspectral image denoising, 3D MRI tomography, and image classification.IEEE Computer Society2024-12-0110570477IEEE Transactions on Pattern Analysis and Machine Intelligence461210337 to 103480162-8828https://doi.org/10.1109/TPAMI.2024.34505751838177; 1730574; 1911094Tensor DecompositionMatrix FactorizationLow-Rank CompletionDeep NetworkSelf-Supervised LearningNational Science Foundation