# 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.

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