Multi Channel Self Navigated Motion Correction

INTRODUCTION In this work we explore the possibility of self navigation in a conventional TSE sequence using the correlation of adjacent sets of k-space lines. The method relies on the assumption that very little motion occurs during a single echotrain and that an extended FOV in the phase encoding direction has been acquired. Further, it requires that the phase encoding order of each echotrain be related by a simple shift in k-space. If a multichannel receive coil is used then the FOV constraint can be relaxed. THEORY Rigid-body motion between two images m1 and m2 can be detected using cross-correlation. If m2 is just a shifted version of m1 (with offsets x0 and y0) then the cross-correlation function C(kx,ky) is a Dirac delta function (offset from the origin by x0 and y0) convolved with the Fourier transform of the magnitude squared of M1(kx,ky). The effect of I{|M1(kx,ky)|} can be removed if we use: ( ) ( ) [ ] ( ) o y o x y x y k x k i k , k C arg i y x w e e k , k C + ⋅ = = [1]