High resolution spectral estimation through localized polynomial approximation

Autoregressive-moving-average models are not adequate for most tomographic imaging reconstruction problems. Consequently, the high-resolution capability being sought is lost when these models are used. In this work, a model based on localized polynomial approximation of the spectrum is proposed to solve this class of spectral estimation problems. A method for finding the model parameters is given, which uses linear prediction theory, matrix eigendecomposition and least-squares fitting. Numerical simulation results are presented to demonstrate its high-resolution capability. It is concluded that the proposed model has a clear advantage over existing models for Gibbs free recovery of piecewise continuous spectra when only limited data are available.