The artifact you are describing is called the Nyquist N/2 Ghost. It occurs with echo-planar imaging sequences that have a zig-zag trajectory through k-space. In head MRI it is sometimes referred to as the "Three Brains Artifact".
EPI pulse sequences are composed of a train of echoes, one echo generated for each line of k-space traversed. In zig-zag acquisition, every second echo is acquired in an alternate direction. For image reconstruction, even numbered echoes must be time-reversed so that match the odd numbered echoes before Fourier transformation.
If the forward and backward echoes are not perfect mirror images of each other, then artifacts are introduced into the image processing. Even a simple delay of the start of the first echo will be propagated into all later echoes resulting in slight timing differences between the peaks of odd- and even-numbered echoes. When the Fourier transform is performed, this phase error results in signal intensity displaced in the phase-encode direction halfway across the image. If there are N pixels across the FOV, this aliased ghost appears shifted N/2 pixels relative to the main image positioned at the correct location.
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N/2 ghost correction is now usually automated and invisible to the user. However, options exist on some scanners for large array (32+channel) coils where local instabilities may cause ghost-correction algorithms to fail.
An EPI pulse sequence called fly-back EPIfly-back EPI uses all positive or all negative readout gradients, eliminating zig-zag phase errors, and is N/2-ghost free. However, fly-back EPI places much higher demands on gradients and switching rate is limited because of peripheral nerve stimulation. Additionally, because the time interval between readout periods is increased, increasing spatial distortion is traded for the elimination of N/2 ghosts.
Buonocore MH, Gao L. Ghost artifact reduction for echo planar imaging using image phase correction. Magn Reson Med 1997; 38:89-100.
Yang QX, Posse S, Le Bihan D, Smith MB. Double-sampled echo-planar imaging at 3 Tesla. J Magn Reson 1996; 113:145-150.