# Aliasing (Wrap-around artifacts)

## Origin

Aliasing or wrap-around corresponds to overlapping on the opposite side of the image of signals outside of the FOV. It is caused by a corruption in the spatial encoding of objects outside the FOV which cannot be distinguished from objects inside the FOV. It results in a spatial mismapping to the opposite side of the image.
Although this artifact can occur in both the frequency and the phase-encode directions, it is actually only an issue in the phase-encode direction. (We will see later how to overcome aliasing easily in the frequency-encode direction, without any penalties).

The range of meaningful phase values is -180° to +180°. It can be represented as the angle corresponding to a position on a circle. A phase of 180° is equivalent to -180°, 200° is equivalent to -160° (200° - 360°), 220° is equivalent to -140° etc...
Phase-encoding consists in modifying the phase of spins in a direction of the slice plane.The phase shifts, ranging from -180° and + 180° at the first encoding step, are assigned to cover the FOV. The next phase-encoding steps use larger ranges which are always a multiple of -180° / + 180° (-360° / + 360°, -540° / + 540° etc...).

If an object extends outside the FOV, it will experience a phase shift (because the phase-encoding gradient is applied on the whole body) but its value will be outside the range. For example, if we consider the first encoding step, the phase shift will be less than -180+ or greater than +180°. Therefore, these values outside the range will be spatially mismapped (remember 200° is equivalent to -160°...) : the reconstruction will produce images with an overlapping of the objects outside the FOV on the opposite side of the image.

## Remedies

Many methods exist for managing aliasing. One way to deal with wrap-around is to swap the frequency-encode and phase-encode directions so that the phase-encode direction is oriented in the shorter dimension of the body part to image. The advantage is that this orientation allows for the use of a rectangular matrix with fewer phase-encoding steps but the same spatial resolution. However, it also modifies other artifacts (ghost images, chemical shift artifacts...) limiting the usefulness of this technique.

Aliasing does not occur if the FOV completely encompasses the body part to be explored in the phase-encode direction. However, increasing the FOV and keeping the same spatial resolution require increasing the number of phase-encoding steps with an acquisition time penalty.

The no-phase wrap method eliminates aliasing without any time or spatial resolution penalties but with a decreased signal to noise ratio. It combines:

• FOV doubling in the phase-encode direction
• Doubling of the number of phase-encoding steps (to keep the samespatial resolution)
• Cutting in half the number of averagings (to keep the same scan time, while reducing the signal to noise ratio)
• Displaying the image on the user-defined FOV

## Aliasing in frequency encoding direction

### Aliasing in frequency encoding direction

Wrap-around can also theoretically occur in the frequency-encode direction. A high-frequency signal can be misinterpreted as a signal of lower frequency due to an inadequate sampling. To avoid frequency aliasing, the sampling rate of the MR signal must be performed at least twice as rapidly as the highest frequency expected. This critical sampling rate is called the Nyquist frequency.

In modern MR scanners, frequency aliasing is eliminated by :

• An oversampling of data during MR signal digitizing
• And/or using a bandpass filter which removes the higher frequencies

These methods have no penalties in terms of scan time or image quality.