Talk by Misha Kilmer, Tufts University

Regularization and Compression via Tensor Dictionaries

Abstract

Over the course of his impressive career to date, Per Christian Hansen’s contributions to the algorithms and analysis for the regularization of ill posed problems have been comprehensive in nature. Indeed, my own research has been greatly influenced by his work, and the subjects of our prior joint work have varied considerably. Therefore, I will focus this talk on one small piece of this body of work that is recent and therefore perhaps less well known. Specifically, I will talk about work that has come about as part of a recent project with Per Christian and one of his former students, Sara Soltani, on tensor patch dictionary learning. I will discuss the dictionary learning problem and the use of the dictionaries in applications such as X-ray CT reconstruction [1], image deblurring, and image compression.

References

[1] Sara Soltani, Misha E. Kilmer, Per Christian Hansen, “A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction,” BIT Numer Math, Volume 56, Issue 4, pp 1425–1454, Dec. 2016.