High-resolution inversion of finite Fourier transform data through a localised polynomial approximation

The authors address the problem of high-resolution inversion of finite Fourier transform data, which is frequently encountered in tomographic image reconstruction. A new parametric modelling approach, which uses an adaptive localised polynomial approximation model of the object function, is proposed to overcome the Gibbs artifact and the limited-resolution problem associated with conventional FFT methods. An algorithm for finding the model parameters is given which makes use of linear prediction theory, singular-value decomposition and least-squares fitting methods. Reconstruction results from simulated and real magnetic resonance experimental data are also presented to demonstrate its capability for Gibbs ringing reduction and resolution enhancement.