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

For reconstruction of a nonnegative 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.