Figure 3: Retrospective motion correction of a structural scan with instructed movement (Table 1: subject 2, trial 4) with moderate motion of 1-2mm (x,y,z) and 1-2deg (θ,ϕ,ψ). Tracking curves for CWLs and NAVs (red, blue respectively) show high degree of similarity (low mean absolute difference, MAD), with largest discrepancy (gray) in y-translations. A substantial increase to visual sharpness (e-l) is evident after retrospective correction using either tracking method. Both methods lead to an increase to average edge strength (AES) of 12.8/9.9% for CWLs and NAVs, respectively.

Figure 1: Measured wire loop signal $$$\mathit{v}_i(t)$$$ for part of a navigator consisting of a weighted sum of columns of $$$\dot{\tilde{\pmb{\mathit{G}}}}(t)$$$, which resemble filtered time derivatives of gradient activity, and are found by sampling the sequence in a static phantom pre-scan with only one active gradient component $$$\mathit{g}_x(t)$$$, $$$\mathit{g}_y(t)$$$, $$$\mathit{g}_z(t)$$$, or active RF. Each wire loop ($$$i=[1,2,\ldots ,I]$$$) measures a unique weighted sum dependent on loop position, orientation, and geometry.