Artifacts
MR physics: Image artifacts - characterization and correction
MR images often contain distortions and spurious features which are collectively described as artifacts. In many cases, artifacts can be traced to sampling issues in k-space. Some simple examples are: (i) inadequate sampling in one dimension (
too large), leading to signal wrap-around or aliasing; (ii) abrupt truncation of the sampling at high spatial frequencies where the object has energy beyond the truncation point, leading to Gibbs ringing at edges in the image; and (iii) spurious signal at isolated time points during data acquisition, which introduces excessive energy at specific spatial frequencies and leads to striping across the image. These and other artifacts are well described in a comprehensive review on the subject [29].
Efforts to characterize and to reduce these artifacts inevitably involve linear systems theory applied in the spatial frequency domain. Below, the specific case of imaging an axial slice through the abdomen of a healthy volunteer is considered as an illustrative case. The abdomen moves during the acquisition as the subject breathes, and artifacts, in this situation `ghosts', appear if motion is ignored in the imaging strategy (Fig. 5a).
A very simple model of the motion in this volume, particularly the motion of the chest wall, is a sinusoidal bulk displacement in the anterior-posterior direction (the y direction in this discussion) of amplitude A and period 
s. Consider the case of spin-warp imaging, where k-space is filled in a grid pattern (sec. iii-B.2). Conceptually, the 
th horizontal line in the grid is acquired by first exciting the slice, and then moving to 
. Data for all 
values corresponding to that 
is acquired shortly thereafter. If, however, the object represented by the magnetization distribution 
has shifted in y by an amount 
at the time the spatial frequency 
is encoded, 
must be replaced by 
in Eq. 7 for that acquisition. By a change of variables, one can see that this introduces an additional phase term 
for that k-space line. Every TR, the index 
is incremented and a new phase error is introduced depending on the position shift 
. In Fig. 5, TR=700 ms so that an entire image acquisition consisting of 128 
encodes requires 90 s corresponding to about 18 breathing cycles. Based on the model, 
across the 
dimension. Thus, 18 periods of phase variation are introduced across 
. Mathematically, the motion-corrupted k-space representation of the slice, 
is given by
where S is the true representation of the slice [30].
To consider the effect on the resultant image, one takes the Fourier transform; the result is the correct image convolved in the y-dimension by a series of narrow point spread functions spaced by (TR/
[30]. The result is a series of image ghosts of various intensities at these shifted positions. The ghosts can produce severe image degradation (Fig. 5a).
Figure 5: Images of an axial slice through the abdomen of a healthy volunteer. Imaging parameters are as follows: TR=0.7 s; TE=48 ms; FOVx=FOVy= 36 cm; 
mm; slice thickness=10 mm; field strength = 1.5 T; image acquisition time is 90 s for each of (a) and (b) and 13 s for (c). For images (a) and (b), the subject is breathing regularly with a respiratory period of about 5 s. Image (c) is a breath-held acquisition. Image (a) is acquired by incrementing 
systematically from -
/2 to 
/2; (b) is acquired by ordering acquisition at different 
based on concurrent measures of chest expansion so that displacement versus 
is given by Fig. 6. (c) Breath-held acquisition using a fast spin-echo sequence where 8 lines in the 
dimension are acquired in each TR interval.
This kind of artifact can be reduced significantly by using a priori information about the object's position as each line in k-space is scanned. For instance, one can measure the chest expansion during the acquisition with a transducer. The strategy is to scan the lines out-of-order so that the displacement will vary monotonically with 
[31] (Fig. 6). Assuming a linear relation between the y displacement and 
, the k-space representation of the slice is now
where 
is defined in Fig. 3. The resulting image is the original object convolved in y by a single blurring point spread function. This method has been used in Fig. 5b to improve significantly the depiction of abdominal anatomy in the presence of respiratory motion.
Figure 6: k-space filling strategy to reduce motion artifacts. (a) Displacements of the chest are measured at the time of each acquisition of a line in k space. In (b), instead of the standard strategy of incrementing 
from -
to 
over the duration of the image scan, measures of displacement are used to select the appropriate 
value at that instant so that displacement varies monotonically with 
.
The general strategy here is to guide the k-space filling pattern with prior knowledge of temporal changes in the MR signal from the volume of interest so that modulation of the true k-space representation varies as gradually and smoothly as possible with 
and 
. The result is a point spread function with a single narrow peak. This strategy has been successfully applied in many MR imaging situations where image contrast varies over the duration of k-space filling.
k-space re-ordering is just one example of a broad range of motion correction schemes developed in MRI. Some other approaches include data correction follow
