The k-space is an extension of the concept of Fourier space that is well known in imaging. In MR imaging the k-space is a temporary memory of the spatial frequency information in two or three dimensions of an object; the k-space is defined by the space covered by the phase and frequency encoding data.
The relation between K-space data and image data is the Fourier Transformation. The data acquisition matrix contains raw image data before the image processing. In 2 dimensional Fourier transformation imaging, a line of data corresponds to the digitized MRI signal at a particular phase encoding level. The position in k-space is directly related to the gradient across the object being imaged. By changing the gradient over time, the k-space data are sampled in a trajectory through Fourier space at each point until it is filled.

See also Spatial Frequency and Raw Data.

Optional component of the computer system used to perform Fourier transformations to accelerate the processing of the received numerical data relative to the MR imaging process, to speed them up.

Chemical shift depends on the nucleus and its environment and is defined as nuclear shielding / applied magnetic field. Nuclei are shielded by a small magnetic field caused by circulating electrons, termed nuclear shielding. The strength of the shield depends on the different molecular environment in that the nucleus is embedded. Nuclear shielding is the difference between the magnetic field at the nucleus and the applied magnetic field.
Chemical shift is measured in parts per million (ppm) of the resonance frequency relative to another or a standard resonance frequency.
The major part of the MR signal comes from hydrogen protons; lipid protons contribute a minor part. The chemical shift between water and fat nuclei is about 3.5 ppm (~220 Hz; 1.5T). Through this difference in resonance frequency between water and fat protons at the same location, a misregistration (dislocation) by the Fourier Transformation take place, when converting MR signals from frequency to spatial domain. This effect is called chemical shift artifact or chemical shift misregistration artifact.

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

During frequency encoding, fat protons precess slower than water protons in the same slice because of their magnetic shielding. Through the difference in resonance frequency between water and fat, protons at the same location are misregistrated (dislocated) by the Fourier transformation, when converting MRI signals from frequency to spatial domain. This chemical shift misregistration cause accentuation of any fat-water interfaces along the frequency axis and may be mistaken for pathology. Where fat and water are in the same location, this artifact can be seen as a bright or dark band at the edge of the anatomy.
Protons in fat and water molecules are separated by a chemical shift of about 3.5 ppm. The actual shift in Hertz (Hz) depends on the magnetic field strength of the magnet being used. Higher field strength increases the misregistration, while in contrast a higher gradient strength has a positive effect. For a 0.3 T system operating at 12.8 MHz the shift will be 44.8 Hz compared with a 223.6 Hz shift for a 1.5 T system operating at 63.9 MHz.

For artifact reduction helps a smaller water fat shift (higher bandwidth), a higher matrix, an in phase TE or a spin echo technique. Since the misregistration offset is present in the read out axis the patient may be rescanned with this axis parallel to the fat-water interface. Steeper gradient may be employed to reduce the chemical shift offset in mm. Another strategy is to employ specialized pulse sequences such as fat saturation or inversion recovery imaging. Fat suppression techniques eliminate chemical shift artifacts caused by the lack of fat signal.

See also Black Boundary Artifact and Magnetic Resonance Spectroscopy.

Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in digital signal processing. This operation is mostly used together with Fourier transformations for MRI signal / image processing.