Fig. 1.

Demonstration of the null space problem using central Cartesian navigators. (a) One frame of a numerical phantom and (b) a spatiotemporal slice through the dotted line. Spatiotemporal slices after projecting the phantom onto the subspace SΦ̂ estimated from (c) horizontal and (d) vertical Cartesian navigators through the k-space origin. The vertical translation of the gray circle is not captured by the horizontal navigator, and the horizontal translational of the white circle is not captured by the vertical navigator.