Revisiting a Fast Newton Solver for a 2-D Spectral Estimation Problem: Computations with the Full Hessian

Abstract

Spectral estimation plays a fundamental role in frequency-domain identification and related signal processing problems. This paper revisits a 2-D spectral estimation problem formulated in terms of convex optimization. More precisely, we work with the dual optimization problem and show that the full Hessian of the dual function admits a Toeplitz-block Toeplitz structure which is consistent with our finding in a previous work. This particular structure of the Hessian enables a fast inversion algorithm in the solution of the dual optimization problem via Newton's method whose superior speed of convergence is illustrated via simulations.