Motion artifact reduction in MRI through generalized DFT

This paper presents a method that dramatically reduces artifacts caused by respiratory (and similar types of) patient motion in magnetic resonance imaging (MRI). The basis for the method is the observation that affine deformations of an object will correspond to a different but unique affine coordinate transform (plus phase shift) of the Fourier representation of the object. The resulting sample points will be irregularly distributed prohibiting the use of standard IFFT to reconstruct the object. The object can however be reconstructed through the use of a weighted regularized pseudo inverse. A standard pseudo inverse is, however, not possible due to excessive computational demands. For this reason a novel fast sequential pseudo inverse algorithm is also presented. Significantly improved results are obtained on both synthetic and clinical data.