Advanced Image Reconstruction Methods in MRI

This chapter provides a tutorial overview of advanced image reconstruction methods used in MRI. The term “advanced” is used loosely to refer to the class of nonFourier reconstruction methods developed for handling the inverse problem with limited Fourier samples. We will consider two specific cases: (a) the superresolution reconstruction problem (associated with limited Fourier samples collected at the Nyquist rate) and (b) the parallel imaging problem (arising when Fourier samples are collected at sub-Nyquist rates, using multiple nonuniform receiver channels).