DELTA: Deep Low-Rank Tensor Representation for Multi-Dimensional Data Recovery

Area of Science:

• Multidimensional Data Analysis
• Machine Learning
• Signal Processing

Background:

• Low-rank tensor recovery methods, like tensor singular value decomposition (t-SVD), leverage data's low-dimensional structure.
• Existing t-SVD approaches often use linear or fully connected network (FCN) based nonlinear transforms, promoting global low-rankness.
• These methods may not fully exploit complex multi-subspace data structures.

Purpose of the Study:

• To propose a novel nonlinear transform within the t-SVD framework to capture long-range dependencies and diverse patterns across multiple data subspaces.
• To develop a low-rank self-representation layer that exploits multi-subspace structures for improved tensor representation.
• To enhance the accuracy and performance of multi-dimensional data recovery.

Main Methods:

• Introduced a nonlinear transform for richer data representation beyond FCNs.
• Developed a low-rank self-representation layer minimizing the nuclear norm of a self-representation tensor.
• Proposed the DEep Low-rank Tensor representAtion (DELTA) framework.

Main Results:

• DELTA captures richer, more nuanced representations by exploiting multiple subspaces.
• The method achieves superior performance in tensor completion, robust tensor completion, and spectral snapshot imaging.
• Experiments on real-world data confirm DELTA's effectiveness over existing methods.

Conclusions:

• The DELTA framework offers a significant advancement in low-rank tensor recovery.
• Its ability to jointly characterize multiple subspaces leads to more accurate data representation and recovery.
• DELTA demonstrates superior performance across various multi-dimensional data recovery applications.