# Low Displacement Rank Dictionaries

Displacement structure^{1} is a generic procedure to quantify the level structure in a matrix. It defines a certain operation (displacement operator) that transform structured matrices into low-rank matrices. The displacement structure framework also provides **fast computational algorithms** for operations involving these structured matrices.

Besides coping with explicit families of structured matrices like Toeplitz, Hankel, Vandermonde and Cauchy, it also manages to identify **implicit structure** like the inverse or products of structured matrices.

This work was developed during my Master’s degree:

C. F. Dantas, “Learning Structured Dictionaries.” At University of Campinas, 2016.

It includes a black-and-white image denoising demo.

Related slides here.

T. Kailath, S.Y. Kung, M. Morf, “Displacement ranks of a matrix”. 1979. ↩