Water and fat signals being in or out of phase result from the FFE method and the slight difference in resonance frequencies of the protons. It can cause black "outlining" of tissues and decrease in signal from voxel containing both water and fat. At 1.5 T, the water and fat signal are in phase when TE is an even multiple, and out of phase when TE is an odd multiple of 2.3 ms.
1.5T: OUT of PHASE = 2.3, 6.9, 11.5, 16.1, 20.7 ms
1.0T: OUT of PHASE = 3.5, 10.4, 17.3, 24.2 ms
0.5T: OUT of PHASE = 6.9, 20.7 ms

See also Opposed Phase Image, and Dixon.

Oversampling is the increase in data to avoid aliasing and wrap around artifacts. Aliasing is the incorrectly mapping of tissue signal from outside the FOV to a location inside the FOV. This is caused by the fact, that the acquired k-space frequency data is not sampled density enough.
Oversampling in frequency direction, done by increasing the sampling frequency, prevents this aliasing artifact. The proper frequency based on the sampling theorem (Shannon sampling theorem/Nyquist sampling theorem) must be at least twice the frequency of each frequency component in the incoming signal. All frequency components above this limit will be aliased to frequencies between zero and half of the sampling frequency and combined with the proper signal information, which creates the artifact. Oversampling creates a larger field of view, more data needs to be stored and processed, but this is for modern MRI systems not a real problem. Oversampling in phase direction (no phase wrap), to eliminate wrap around artifacts, by increasing the number of phase encoding steps, results in longer scan/processing times.

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).

(PS) Excitation technique applying repeated RF pulses in times comparable to or shorter than T1. Incomplete T1 relaxation leads to reduction of the signal amplitude; there is the possibility of generating images with increased contrast between regions with different relaxation times.
Although partial saturation is also commonly referred to as saturation recovery, that term should properly be reserved for the particular case of partial saturation in which recovery after each excitation effectively takes place from true saturation. A GRE sequence where α = 90° is identical to the partial saturation or saturation recovery pulse sequence.
It does not directly produce images of T1. However, since the measured signal will depend on T1, the method generates contrast between regions with different relaxation times. If T2 and/or T2 effects are minimized through the use of a short echo time TE, the result is a T1 weighted image. It is not a T1 image due to the possible presence of spin density and T2 effects as well as the nonlinear dependence on T1.
The change in signal from a region resulting from a change in the interpulse time, TR, can be used to calculate T1 for the region.

(PWI - Perfusion Weighted Imaging) Perfusion MRI techniques (e.g. PRESTO - Principles of Echo Shifting using a Train of Observations) are sensitive to microscopic levels of blood flow. Contrast enhanced relative cerebral blood volume (rCBV) is the most used perfusion imaging. Both, the ready availability and the T2* susceptibility effects of gadolinium, rather than the T1 shortening effects make gadolinium a suitable agent for use in perfusion imaging. Susceptibility here refers to the loss of MR signal, most marked on T2* (gradient echo)-weighted and T2 (spin echo)-weighted sequences, caused by the magnetic field-distorting effects of paramagnetic substances.
T2* perfusion uses dynamic sequences based on multi or single shot techniques. The T2* (T2) MRI signal drop within or across a brain region is caused by spin dephasing during the rapid passage of contrast agent through the capillary bed. The signal decrease is used to compute the relative perfusion to that region. The bolus through the tissue is only a few seconds, high temporal resolution imaging is required to obtain sequential images during the wash in and wash out of the contrast material and therefore, resolve the first pass of the tracer. Due to the high temporal resolution, processing and calculation of hemodynamic maps are available (including mean transit time (MTT), time to peak (TTP), time of arrival (T0), negative integral (N1) and index.
An important neuroradiological indication for MRI is the evaluation of incipient or acute stroke via perfusion and diffusion imaging. Diffusion imaging can demonstrate the central effect of a stroke on the brain, whereas perfusion imaging visualizes the larger 'second ring' delineating blood flow and blood volume. Qualitative and in some instances quantitative (e.g. quantitative imaging of perfusion using a single subtraction) maps of regional organ perfusion can thus be obtained.
Echo planar and potentially echo volume techniques together with appropriate computing power offer real time images of dynamic variations in water characteristics reflecting perfusion, diffusion, oxygenation (see also Oxygen Mapping) and flow.
Another type of perfusion MR imaging allows the evaluation of myocardial ischemia during pharmacologic stress. After e.g., adenosine infusion, multiple short axis views (see cardiac axes) of the heart are obtained during the administration of gadolinium contrast. Ischemic areas show up as areas of delayed and diminished enhancement. The MRI stress perfusion has been shown to be more accurate than nuclear SPECT exams. Myocardial late enhancement and stress perfusion imaging can also be performed during the same cardiac MRI examination.