Low Rank Tensor Completion

Low-rank tensor completion aims to recover missing entries in a high-dimensional tensor by exploiting its underlying low-rank structure, crucial for handling incomplete data in various applications. Current research focuses on developing efficient algorithms, often based on non-convex regularizers or novel tensor norms (like tubal rank or tensor train rank), to improve accuracy and computational speed, particularly under challenging conditions like very sparse observations. These advancements are impacting fields such as image processing, traffic data analysis, and remote sensing by enabling more robust and accurate data imputation and reconstruction from incomplete datasets. The development of parameter-free models and the incorporation of numerical priors further enhance the practical applicability and performance of these methods.