Mathematics for Imaging, Vision and their Applications

Higher-order tensors are suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer vision. However, classical low-rank tensor representations can solely represent multi-dimensional discrete data on meshgrid, which hinders their potential applicability in many scenarios beyond meshgrid. In this talk, we discuss the recent development of tensor representations in data science. Both theoretical results and numerical examples are presented to demonstrate the usefulness of tensor representations.