The l1 measure of image reconstruction subject to motion corrupted k-space data

For reconstruction of a non-negative real valued object based on scanned data in the k-space, it is shown that the l1 norm of the original motionless object is minimum among that of all objects with combined translational and rotational motions and is a sensitive measure of the object motions. These results provide an insight and theoretical fundamental for applying the l1 optimization to the motion correction problem for image reconstruction in various practical applications.