Nuclear Norm

The nuclear norm, a mathematical concept representing the sum of singular values of a matrix (or its generalization to tensors), is central to low-rank matrix/tensor recovery and completion problems. Current research focuses on developing efficient algorithms, often employing iterative reweighting schemes or alternating direction method of multipliers (ADMM), to minimize nuclear norm-based objective functions, incorporating techniques like Haar wavelet transforms or quaternion algebra to improve performance in specific applications such as image processing and remote sensing. This work has significant implications for various fields, enabling improved solutions in areas like image denoising, MRI reconstruction, and knowledge graph completion by leveraging the low-rank structure inherent in many real-world datasets.