DeepTensor: Low-Rank Tensor Decomposition With Deep Network Priors.

Area of Science:

• Computational mathematics
• Machine learning
• Signal processing

Background:

• Classical low-rank decomposition methods like SVD and PCA struggle with nonlinear structures and non-Gaussian noise.
• Deep generative networks (DNs) offer implicit regularization, enabling capture of complex signal patterns.

Purpose of the Study:

• To introduce DeepTensor, a novel framework for efficient low-rank tensor decomposition using deep generative networks.
• To demonstrate DeepTensor's robustness and computational efficiency compared to existing methods.

Main Methods:

• Decomposing tensors into low-rank factors generated by self-supervised deep networks.
• Minimizing mean-square approximation error during network training.
• Evaluating performance across hyperspectral image denoising, 3D MRI tomography, and image classification.

Main Results:

• DeepTensor effectively captures nonlinear signal structures missed by SVD and PCA.
• The framework exhibits robustness to various data distributions, unlike SVD and PCA.
• Achieved a 6 dB SNR improvement in Poisson noise denoising and 60x speedup in 3D tensor decomposition.

Conclusions:

• DeepTensor provides a computationally efficient and robust alternative to traditional low-rank decomposition techniques.
• The implicit regularization of deep networks is key to uncovering complex, nonlinear data patterns.
• DeepTensor demonstrates significant advantages in real-world applications requiring efficient and accurate tensor analysis.