Quick Overview
Please note that there are different common names for this MRI artifact.

Aliasing is an artifact that occurs in MR images when the scanned body part is larger than field of view (FOV). As a consequence of the acquired k-space frequencies not being sampled densely enough, whereby portions of the object outside of the desired FOV get mapped to an incorrect location inside the FOV. The cyclical property of the Fourier transform fills the missing data of the right side with data from behind the FOV of the left side and vice versa. This is caused by a too small number of samples acquired in, e.g. the frequency encoding direction, therefore the spectrums will overlap, resulting in a replication of the object in the x direction.
Aliasing in the frequency direction can be eliminated by twice as fast sampling of the signal or by applying frequency specific filters to the received signal.
A similar problem occurs in the phase encoding direction, where the phases of signal-bearing tissues outside of the FOV in the y-direction are a replication of the phases that are encoded within the FOV. Phase encoding gradients are scaled for the field of view only, therefore tissues outside the FOV do not get properly phase encoded relative to their actual position and 'wraps' into the opposite side of the image.

Use a larger FOV, RFOV or 3D Volume, apply presaturation pulses to the undesired tissue, adjust the position of the FOV, or select a small coil which will only receive signal from objects inside or near the coil. The number of phase encoding steps must be increased in phase direction, unfortunately resulting in longer scan times.
When this is not possible it can be corrected by oversampling the data. Aliasing is eliminated by Oversampling in frequency direction. No Phase Wrap (Foldover Suppression) options typically correct the phase encoding by doubling the field of view, doubling the number of phase encodes (to keep resolution constant) and halving the number of averages (to keep scan time constant) then discarding the additional data and processing the image within the desired field of view (but this is more time consuming).
Tissue outside this doubled area can be folded nevertheless into the image as phase wrap. In this case combine more than 2 number of excitations / number of signal averages with foldover suppression.
See also Aliasing, Foldover Suppression, Oversampling, and Artifact Reduction - Aliasing.

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(BW) Bandwidth is a measure of frequency range, the range between the highest and lowest frequency allowed in the signal. For analog signals, which can be mathematically viewed as a function of time, bandwidth is the width, measured in Hertz of a frequency range in which the signal's Fourier transform is nonzero.

A higher bandwidth is used for the reduction of chemical shift artifacts (lower bandwidth - more chemical shift - longer dwell time - but better signal to noise ratio). Narrow receive bandwidths accentuate this water fat shift by assigning a smaller number of frequencies across the MRI image. This effect is much more significant on higher field strengths. At 1.5 T, fat and water precess 220 Hz apart, which results in a higher shift than in Low Field MRI.
Lower bandwidth (measured in Hz) = higher water fat shift (measured in pixel shift).

See also Aliasing, Aliasing Artifact, Frequency Encoding, and Chemical Shift Artifact.

Brain imaging, magnetic resonance imaging of the head or skull, cranial magnetic resonance tomography (MRT), neurological MRI - they describe all the same radiological imaging technique for medical diagnostic.
Magnetic resonance imaging of the human brain includes the anatomic description and the detection of lesions. Special techniques like diffusion weighted imaging, functional magnetic resonance imaging (fMRI) and spectroscopy provide also information about the function and chemical metabolites of the brain. MRI provides detailed pictures of brain and nerve tissues in multiple planes without obstruction by overlying bones. Brain MRI is the procedure of choice for most brain disorders. It provides clear images of the brainstem and posterior brain, which are difficult to view on a CT scan. It is also useful for the diagnosis of demyelinating disorders (disorders such as multiple sclerosis (MS) that cause destruction of the myelin sheath of the nerve).
With this noninvasive procedure also the evaluation of blood flow and the flow of cerebrospinal fluid (CSF) is possible. Different MRA methods, also without contrast agents can show a venous or arterial angiogram. MRI can distinguish tumors, inflammatory lesions, and other pathologies from the normal brain anatomy. However, MRI scans are also used instead other methods to avoid the dangers of interventional procedures like angiography (DSA - digital subtraction angiography) as well as of repeated exposure to radiation as required for computed tomography (CT) and other X-ray examinations.
A (birdcage) bird cage coil achieves uniform excitation and reception and is commonly used to study the brain. Usually a brain MRI procedure includes FLAIR, T2 weighted and T1 weighted sequences in two or three planes.

See also Fetal MRI, Fluid Attenuation Inversion Recovery (FLAIR), Perfusion Imaging and High Field MRI.
See also Arterial Spin Labeling.

(CSI) Chemical shift imaging is an extension of MR spectroscopy, allowing metabolite information to be measured in an extended region and to add the chemical analysis of body tissues to the potential clinical utility of Magnetic Resonance. The spatial location is phase encoded and a spectrum is recorded at each phase encoding step to allow the spectra acquisition in a number of volumes covering the whole sample. CSI provides mapping of chemical shifts, analog to individual spectral lines or groups of lines.
Spatial resolution can be in one, two or three dimensions, but with long acquisition times od full 3D CSI. Commonly a slice-selected 2D acquisition is used. The chemical composition of each voxel is represented by spectra, or as an image in which the signal intensity depends on the concentration of an individual metabolite. Alternatively frequency-selective pulses excite only a single spectral component.
There are several methods of performing chemical shift imaging, e.g. the inversion recovery method, chemical shift selective imaging sequence, chemical shift insensitive slice selective RF pulse, the saturation method, spatial and chemical shift encoded excitation and quantitative chemical shift imaging.

See also Magnetic Resonance Spectroscopy.