Padé methods for reconstruction and feature extraction in magnetic resonance imaging

Methods utilizing Padé approximants are investigated for implementation with magnetic resonance imaging data and are presented both for direct image reconstruction and for feature extraction. Padé approximants are a numerical tool that can be used to accelerate the convergence of a slowly converging sequence by estimating the fully converged sequence values from early data points. Padé approximants can be calculated directly from k-space data by solving a set of linear matrix equations to produce signal values for any desired location in the image domain. This gives an estimate of the fully converged signal intensity at each pixel location in the image, raising the possibility of reconstructing a better estimate of the object from a reduced data set. These methods have been tested on phantom and human data both for image reconstruction and for feature extraction. In image reconstruction, considerable convergence acceleration can be achieved, with steep intensity boundaries reproduced in keeping with higher resolution reconstructions and oscillatory truncation artifact characteristic of Fourier reconstruction removed. The convergence acceleration is variable and there is the possibility of fine detail suppression when insufficient data are included. The use of Padé methods as a tool for feature extraction has shown good agreement with extraction from high-resolution reference data. In this approach the edge information comes intrinsically from Padé reconstruction.