Inhomogeneity is the degree of lack of homogeneity, for example the fractional deviation of the local magnetic field from the average value of the field. Inhomogeneities of the static magnetic field, produced by the scanner as well as by object susceptibility, is unavoidable in MRI. The large value of gyromagnetic coefficient causes a significant frequency shift even for few parts per million field inhomogeneity, which in turn causes distortions in both geometry and intensity of the MR images.
Manufacturers try to make the magnetic field as homogeneous as possible, especially at the core of the scanner. Even with an ideal magnet, a little inhomogeneity is always left and is caused in addition by the susceptibility of the imaging object. The geometrical distortion (displacement of the pixel locations) are important e.g., for some cases as stereotactic surgery. Displacements up to 3 to 5 mm have been reported. The second problem is the undesired changes in the intensity or brightness of pixels, which may cause problems in determining different tissues and reduce the maximum achievable image resolution.

General strategies for reducing field inhomogeneity induced artifacts:
Increasing the strength of the gradient magnetic field.
Decreasing the echo time.
Improving the image resolution. Phase encoding. Postprocessing.

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.

The MRI device is located within a specially shielded room (Faraday cage) to avoid outside interference, caused by the use of radio waves very close in frequency to those of ordinary FM radio stations.
The MRI procedure can easily be performed through clothing and bones, but attention must be paid to ferromagnetic items, because they will be attracted from the magnetic field. A hospital gown is appropriate, or the patient should wear clothing without metal fasteners and remove any metallic objects like hairpins, jewelry, eyeglasses, clocks, hearing aids, any removable dental work, lighters, coins etc., not only for MRI safety reasons. Metal in or around the scanned area can also cause errors in the reconstructed images (artifacts). Because the strong magnetic field can displace, or disrupt metallic objects, people with an implanted active device like a cardiac pacemaker cannot be scanned under normal circumstances and should not enter the MRI area.
The MRI machine can look like a short tunnel or has an open MRI design and the magnet does not completely surround the patient. Usually the patient lies on a comfortable motorized table, which slides into the scanner, depending on the MRI device, patients may be also able to sit up. If a contrast agent is to be administered, intravenous access will be placed. A technologist will operate the MRI machine and observe the patient during the examination from an adjacent room. Several sets of images are usually required, each taking some minutes. A typical MRI scan includes three to nine imaging sequences and may take up to one hour. Improved MRI devices with powerful magnets, newer software, and advanced sequences may complete the process in less time and better image quality.
Before and after the most MRI procedures no special preparation, diet, reduced activity, and extra medication is necessary. The magnetic field and radio waves are not felt and no pain is to expect.
Movement can blur MRI images and cause certain artifacts. A possible problem is the claustrophobia that some patients experience from being inside a tunnel-like scanner. If someone is very anxious or has difficulty to lie still, a sedative agent may be given. Earplugs and/or headphones are usually given to the patient to reduce the loud acoustic noise, which the machine produces during normal operation. A technologist observes the patient during the test. Some MRI scanners are equipped with televisions and music to help the examination time pass.
MRI is not a cheap examination, however cost effective by eliminating the need for invasive radiographic procedures, biopsies, and exploratory surgery. MRI scans can also save money while minimizing patient risk and discomfort. For example, MRI can reduce the need for X-ray angiography and myelography, and can eliminate unnecessary diagnostic procedures that miss occult disease.

See also Magnetic Resonance Imaging MRI, Medical Imaging, Cervical Spine MRI, Claustrophobia, MRI Risks and Pregnancy.
For Ultrasound Imaging (USI) see Ultrasound Imaging Procedures at Medical-Ultrasound-Imaging.com.

See also the related poll result: 'MRI will have replaced 50% of x-ray exams by'

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

Patient motion is the largest physiological effect that causes artifacts, often resulting from involuntary movements (e.g. respiration, cardiac motion and blood flow, eye movements and swallowing) and minor subject movements.
Movement of the object being imaged during the sequence results in inconsistencies in phase and amplitude, which lead to blurring and ghosting. The nature of the artifact depends on the timing of the motion with respect to the acquisition. Causes of motion artifacts can also be mechanical vibrations, cryogen boiling, large iron objects moving in the fringe field (e.g. an elevator), loose connections anywhere, pulse timing variations, as well as sample motion. These artifacts appear in the phase encoding direction, independent of the direction of the motion.

Motion artifacts can be flipped 90° by swapping the phase//frequency encoding directions.
The artifacts can be reduced by using breath holding, cardiac synchronization or respiratory compensation techniques: triggering, gating, retrospective triggering or phase encoding artifact reduction. Flow effects can be reduced by using gradient moment nulling of the first order of flow, gradient moment rephasing or flow compensation, depending of the MRI system.
Peristaltic motion can be reduced with the intravenous injection of an anti-spasmodic (e.g. Buscopan).
By using multiple averages, respiratory motion can be reduced in the same way that multiple averages increase the signal to noise ratio. Noticeable motion averaging is seen when four averages are obtained, six averages are often as good as respiratory compensation techniques and higher averages will continue to improve image quality.
In some cases will help a presaturation of the anatomy that was generating the motion.

See also Phase Encoded Motion Artifact.

(LE) Myocardial late enhancement in contrast enhanced cardiac MRI has the ability to precisely delineate myocardial scar associated with coronary artery disease. Viability imaging implies evaluating infarcted myocardium to see whether there is enough viable tissue available for revascularization. The reversal of myocardial dysfunction is particularly relevant in patients with depressed ventricular function because revascularization improves long-term survival. In comparison to SPECT and PET imaging, myocardial late enhancement MRI demonstrates areas of delayed enhancement exactly in correlation with the infarcted region.
Viability on cardiac MRI (CMR) is based on the fact that all infarcts enhance vividly 10-15 minutes after the administration of intravenous paramagnetic contrast agents. This enhancement represents the accumulation of gadolinium in the extracellular space, due to the loss of membrane integrity in the infarcted tissue. This phenomenon of delayed hyperenhancement has been proven to correlate with the actual extent of the infarct.
MRI myocardial late enhancement can quantify the size, location and transmural extent of the infarct. If the transmural extent of the infarct (region of enhancement on MRI) is less than 50% of the wall thickness, there will be improved contractility in that segment following revascularization. In areas of hypokinesia, if there is a rim of "black" or non-infarcted myocardium that is not contracting well, it indicates the presence of hibernating myocardium, which is likely to improve after revascularization of the artery supplying that particular territory.
The total duration of a myocardial late enhancement MR imaging protocol for viability is approximately 30 minutes, including scout images, first-pass images, cine images in two planes, and delayed myocardial enhancement images. In order to assess viable myocardium, the gadolinium contrast agent is injected at a dose of 0.15 to 0.2 mmol/kg. After about 10 minutes, short axis and long axis views (see cardiac axes) of the heart are obtained using an inversion prepared ECG gated gradient echo sequence. The inversion pulse is adjusted to suppress normal myocardium. Areas of nonviable myocardium retain extremely high signal intensity, black areas show normal tissue.

For Ultrasound Imaging (USI) see Myocardial Contrast Echocardiography at Medical-Ultrasound-Imaging.com.