(FFT) A particularly fast and efficient computational method of performing a Fourier transformation, which is the mathematical process by which raw data is processed into a usable image.

(SENSE) A MRI technique for relevant scan time reduction. The spatial information related to the coils of a receiver array are utilized for reducing conventional Fourier encoding. In principle, SENSE can be applied to any imaging sequence and k-space trajectories. However, it is particularly feasible for Cartesian sampling schemes. In 2D Fourier imaging with common Cartesian sampling of k-space sensitivity encoding by means of a receiver array enables to reduce the number of Fourier encoding steps.
SENSE reconstruction without artifacts relies on accurate knowledge of the individual coil sensitivities. For sensitivity assessment, low-resolution, fully Fourier-encoded reference images are required, obtained with each array element and with a body coil.
The major negative point of parallel imaging techniques is that they diminish SNR in proportion to the numbers of reduction factors. R is the factor by which the number of k-space samples is reduced. In standard Fourier imaging reducing the sampling density results in the reduction of the FOV, causing aliasing. In fact, SENSE reconstruction in the Cartesian case is efficiently performed by first creating one such aliased image for each array element using discrete Fourier transformation (DFT).
The next step then is to create a full-FOV image from the set of intermediate images. To achieve this one must undo the signal superposition underlying the fold-over effect. That is, for each pixel in the reduced FOV the signal contributions from a number of positions in the full FOV need to be separated. These positions form a Cartesian grid corresponding to the size of the reduced FOV.
The advantages are especially true for contrast-enhanced MR imaging such as dynamic liver MRI (liver imaging) , 3 dimensional magnetic resonance angiography (3D MRA), and magnetic resonance cholangiopancreaticography (MRCP).
The excellent scan speed of SENSE allows for acquisition of two separate sets of hepatic MR images within the time regarded as the hepatic arterial-phase (double arterial-phase technique) as well as that of multidetector CT.
SENSE can also increase the time efficiency of spatial signal encoding in 3D MRA. With SENSE, even ultrafast (sub second) 4D MRA can be realized.
For MRCP acquisition, high-resolution 3D MRCP images can be constantly provided by SENSE. This is because SENSE resolves the presence of the severe motion artifacts due to longer acquisition time. Longer acquisition time, which results in diminishing image quality, is the greatest problem for 3D MRCP imaging.
In addition, SENSE reduces the train of gradient echoes in combination with a faster k-space traversal per unit time, thereby dramatically improving the image quality of single shot echo planar imaging (i.e. T2 weighted, diffusion weighted imaging).

In fast imaging sequences driven equilibrium sensitizes the sequence to variations in T2. This MRI technique turns transverse magnetization Mxy to the longitudinal axis using a pulse rather than waiting for T1 relaxation.
The first two pulses form a spin echo and, at the peak of the echo, a second 90° pulse returns the magnetization to the z-axis in preparation for a fresh sequence. In the absence of T2 relaxation, then all the magnetization can be returned to the z-axis. Otherwise, T2 signal loss during the sequence will reduce the final z-magnetization.
The advantage of this sequence type is, that both longitudinal and also transverse magnetization are back to equilibrium in a shorter amount of time. Therefore, contrast and signal can be increased while using a shorter TR. This pulse type can be applied to other sequences like FSE, GE or IR.

Sequences with driven equilibrium:
Driven Equilibrium Fast Gradient Recalled acquisition in the steady state - DE FGR,
Driven Equilibrium Fourier Transformation - DEFT,
Driven Equilibrium magnetization preparation - DE prep,
Driven Equilibrium Fast Spin Echo - DE FSE.

The process of locating a MR signal by altering the phase of spins in one dimension with a pulsed magnetic field gradient along that dimension prior to the acquisition of the signal.
If a gradient field is briefly switched on and then off again at the beginning of the pulse sequence right after the radio frequency pulse, the magnetization of the external voxels will either precess faster or slower relative to those of the central voxels.
During readout of the signal, the phase of the xy-magnetization vector in different columns will thus systematically differ. When the x- or y- component of the signal is plotted as a function of the phase encoding step number n and thus of time n TR, it varies sinusoidally, fast at the left and right edges and slow at the center of the image. Voxels at the image edges along the phase encoding direction are thus characterized by a higher 'frequency' of rotation of their magnetization vectors than those towards the center.
As each signal component has experienced a different phase encoding gradient pulse, its exact spatial reconstruction can be specifically and precisely located by the Fourier transformation analysis. Spatial resolution is directly related to the number of phase encoding levels (gradients) used. The phase encoding direction can be chosen, e.g. whenever oblique MR images are acquired or when exchanging frequency and phase encoding directions to control wrap around artifacts.