Cartesian sampling is used to refer to data collection with a fixed value of the phase encoding gradient. 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. This is achieved by increasing the distance of sampling positions in k-space while maintaining the maximum k-values.
The Cartesian coordinates are obtained from the polar coordinates by the operations
x = r sin f
y = r cos f
using the trigonometric functions sine and cosine.

(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).

Trigonometric functions are mathematical functions of an angle. There are six basic trigonometric functions (Sine (sin), Cosine (cos), Tangent (tan), Cotangent (cot), Secant (sec), Cosecant (cosec)), commonly defined as ratios of two sides of a right triangle. Used in MRI for Cartesian sampling, to describe radio frequency signals, etc.

The ensemble of raw data points collected during the signal readout. For example, during Cartesian sampling, normally used to refer to data collected with a fixed value of the phase encoding gradient. Also referred to as one line of k-space. In projection reconstruction, the line is radial oriented, while in spiral imaging, it is a spiral.