Research Projects

In recent years, models using tensors have significantly impacted many areas in engineering and science (e.g., BIG data analysis, machine learning, statistics, image processing, and scientific computing). Thus efficient and reliable algorithms for solving such multilinear systems are required. In this regard, efficient tensor decomposition algorithms are necessary for analytic simplicity and computational convenience to calculate tensor inverse and solve the multilinear system. Many of the powerful tools of matrix computations, such as finding the inverse, generalized inverse, and decompositions (SVD, LU, Schur decompositions, etc.) do not, unfortunately, extend in a straightforward manner to tensors of order three or higher. From these perspectives, it is appropriate to explore an infrastructure for tensor decomposition and finding inverses to solve multilinear systems. The main objective of this project is to design fast and efficient algorithms for solving tensor equations and their applications. Specifically, we propose a few effective tensor-based iterative algorithms for computing tensor generalized inverses and their application in color imaging. Then tensor generalized inverses will be used in solving third-order Poisson problems in the framework of the t-product. We further develop a new powerful technique to decompose/factor tensors efficiently and reconstruct the images from blurred images or data sets representing digitized images.