In parallel MR imaging, a reduced data set in the phase encoding direction(s) of k-space is acquired to shorten acquisition time, combining the signal of several coil arrays. The spatial information related to the phased array coil elements is utilized for reducing the amount of conventional Fourier encoding.
First, low-resolution, fully Fourier-encoded reference images are required for sensitivity assessment. Parallel imaging reconstruction in the Cartesian case is efficiently performed by creating one aliased image for each array element using discrete Fourier transformation. The next step then is to create an full FOV image from the set of intermediate images. Parallel reconstruction techniques can be used to improve the image quality with increased signal to noise ratio, spatial resolution, reduced artifacts, and the temporal resolution in dynamic MRI scans.
Parallel imaging algorithms can be divided into 2 main groups:
Image reconstruction produced by each coil (reconstruction in the image domain, after Fourier transform): SENSE (Sensitivity Encoding), PILS (Partially Parallel Imaging with Localized Sensitivity), ASSET.
Reconstruction of the Fourier plane of images from the frequency signals of each coil (reconstruction in the frequency domain, before Fourier transform): GRAPPA.
Additional techniques include SMASH, SPEEDER™, IPAT (Integrated Parallel Acquisition Techniques - derived of GRAPPA a k-space based technique) and mSENSE (an image based enhanced version of SENSE).

(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.

(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.

(FOV) Defined as the size of the two or three dimensional spatial encoding area of the image. Usually defined in units of mm². The FOV is the square image area that contains the object of interest to be measured. The smaller the FOV, the higher the resolution and the smaller the voxel size but the lower the measured signal. Useful for decreasing the scantime is a field of view different in the frequency and phase encoding directions (rectangular field of view - RFOV).
The magnetic field homogeneity decreases as more tissue is imaged (greater FOV). As a result the precessional frequencies change across the imaging volume. That can be a problem for fat suppression imaging. This fat is precessing at the expected frequency only in the center of the imaging volume. E.g. frequency specific fat saturation pulses become less effective when the field of view is increased. It is best to use smaller field of views when applying fat saturation pulses.

Smaller FOV required higher gradient strength and concludes low signal. Therefore you have to find a compromise between these factors. The right choice of the field of view is important for MR image quality. When utilizing small field of views and scanning at a distance from the isocenter (more problems with artifacts) it is obviously important to ensure that the region of interest is within the scanning volume.
A smaller FOV in one direction is available with the function rectangular field of view (RFOV).

See also Field Inhomogeneity Artifact.

(FT) The Fourier transformation is a mathematical procedure to separate out the frequency components of a signal from its amplitudes as a function of time, or the inverse Fourier transformation (IFT) calculates the time domain from the frequency domain. The FT is used to generate the spectrum from the free induction decay or spin echo in the pulse MR technique and is essential to most MR imaging techniques. The Fourier transformation can be generalized to multiple dimensions, e.g. to relate an image to its corresponding k-space representation, or to include chemical shift information in some chemical shift imaging techniques. Fourier transformation analysis allows spatial information to be reconstructed from the raw data.