This paper addresses the problem of motion artifact cancellation in th
e standard 2D-FFT MRI. Although motion is possible in any direction, i
n clinical MRI diagnosis, respiration is considered to be the main cau
se of motion. As a first order of approximation, motion due to respira
tion is assumed to be only in the phase-encoding direction (Y-axis) in
this paper. In the previous approach, the region of a target object i
s assumed to be known and an iterative procedure is required. The prob
lem of the algorithm is the convergence of the iterative (which may ta
ke a lot of time) and still has no guarantee of convergence. To avoid
an iterative procedure, a new constraint is proposed here, with which
the motion component and the true image component can be separated by
a simple algebraic operation. After the Fourier transform of MRI signa
l along the read-out direction (X-direction), the phase of the spectru
m along Y-axis is expressed as an algebraic sum of the motion componen
t and the true image component. On the other hand, when density distri
bution is symmetric along a Y-direction line, such as a slice line on
subcutaneous fat, the phase of the Fourier spectrum along the line is
a linear function of Y-position. Therefore, if the density is symmetri
c, the departure from the linear function of the phase is just the mot
ion component. With this constraint the motion component can be estima
ted and the motion artifact in MRI can be canceled. The algorithm is s
hown to be effective using a phantom with simulated motions in various
cases. When the density distribution along the Y-directional line on
subcutaneous fat is not perfectly symmetric, the accuracy of estimated
motion will be affected to some extent. However, this method is shown
to be still effective in such general case by simulations.