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

Abstract

For reconstruction of a nonnegative real valued object based on scanned data in the k-space, it is shown that the l 1 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 l 1 optimization to the motion correction problem for image reconstruction in various practical applications.

Analysis, algorithms and applications of compressed sensing

“…One of the future directions is to design efficient algorithms and analyze their performance for CPR. Our preliminary results are presented in [145,153].…”