Self-similarity of Fourier domain MRI data

Abstract

This paper presents an overview of our recent research on the self-similar properties of magnetic resonance imaging data in the Fourier domain. The motivation behind our work is to use self-similarity as a constraint towards the spatial resolution enhancement of spatially-limited magnetic resonance images. We describe a fractal-based method over (complex-valued) Fourier transforms of functions with compact support, derived from a fractal-based method in the spatial domain. We show that our fractal-based method can be tailored to perform frequency extrapolation in the frequency domain. Furthermore, we develop a model of the one-dimensional MRI data that shows local self-similarity by drawing a connection to autoregressive modeling. Finally, we present a statistical analysis of two-dimensional k-space MRI data which suggests that MRI Fourier data can be self-similar.