The multidimensional rational covariance extension problems
Coriolis room, Galois building – July 3, 2018 at 02:00 PM.
The rational covariance extension problem is a trigonometric moment problem with several important applications in systems and control, for example in spectral estimation and system identification. The problem, which was originally posed by R.E. Kalman, has been extensively studied in the literature and can be solved using convex optimization.
The problem has the epithet “rational” because the sought solution of the moment problem is a rational function. The reason for this desire is due to the fundamental role that rational functions play in systems and control, for example guaranteeing realizability in terms of a finite-dimensional linear dynamical system. In this talk I will introduce and motivate the interest in the rational covariance extension problem, and then focus on resent work on the multidimensional counterpart. Here, we leverage the convex optimization formulation and generalize this optimization problem to a multidimensional setting. Finally, I will give an example of how this multidimensional theory can be used for binary texture generation, by modeling the texture as the output of a Wiener system.