The Case for T-Product Tensor Decompositions: Compression, Analysis and Reconstruction of Image Data

Most problems in imaging science involve operators or data that are
inherently multidimensional in nature, yet traditional approaches to
modeling, analysis and compression of (sequences of) images involve
matricization of the model or data. In this talk, we discuss ways in
which multiway arrays, called tensors, can be leveraged in imaging
science for tasks such as forward problem modeling, regularization and
reconstruction, video analysis, and compression and recognition of facial
image data. The unifying mathematical construct in our approaches to
these problems is the t-product (Kilmer and Martin, LAA, 2011) and
associated algebraic framework. We will see that the t-product permits
the elegant extension of linear algebraic concepts and matrix algorithms
to tensors, which in turn gives rise to new, highly parallelizable,
algorithms for the imaging tasks noted above.