What is k-space in MRI?

What is k-space in MRI?

k-space is an abstract concept and refers to a data matrix containing the raw MRI data. This data is subjected to mathematical function or formula called a transform to generate the final image.

How do you calculate k-space?

By definition, the value of k-space at a particular kx, ky can be determined by performing two steps: (1) multiplying the image by cos(kxx + kyy) and then (2) summing the value of all the signal across the entire image.

What is k-space trajectory?

You alluded to different trajectories for filling k-space. What are they? k-space for pigeons. Before generation of the MR signal, k-space is just an array of blank cells awaiting the arrival of data. As an analogy, think of it as a box of empty “pigeon holes” waiting to receive “pigeons”.

What is k-space sampling?

In MRI physics, complex values are sampled in k-space during an MR measurement in a premeditated scheme controlled by a pulse sequence, i.e. an accurately timed sequence of radiofrequency and gradient pulses.

What does K stand for in k-space?

wavenumber
k = 1 / λ The wavenumber (k) is therefore the number of waves or cycles per unit distance. Since the wavelength is measured in units of distance, the units for wavenumber are (1/distance), such as 1/m, 1/cm or 1/mm.

What does each point in k-space represent?

Each “star” in k-space is just a data point derived directly from the MR signal. The brightness of each star represents the relative contribution of that star’s unique spatial frequency to the final image. K-space is the Fourier transform of the MR image.

What is k-space in solid state physics?

The k-space represents 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 relationship between k-space data and image data is the Fourier transformation.

Which k-space trajectory starts at the center of k-space?

Here are the rules for moving in k-space: The initial RF excitation pulse (with the slice-selection gradient) is the beginning of the sequence: location is at the center of k-space. A 180° RF pulse causes a jump to the opposite location.

What are the units of k-space?

The wavenumber (k) is therefore the number of waves or cycles per unit distance. Since the wavelength is measured in units of distance, the units for wavenumber are (1/distance), such as 1/m, 1/cm or 1/mm.

What is k-space in condensed matter?

k-space is momentum space. Each x, y and z axis is replaced by the corresponding momentum. As momentum for a particle is Planck’s constant over wavelength, in the convention where h=1, a particle shown moving in k-space is a graph of its momentum instead of it’s position.

Why is Centre of k-space brightest?

There are two reasons the central area of k-space is the brightest. First, the central row (ky = 0) is acquired with no phase-encoding gradient (and hence no destructive wave interference caused by phase-encoding steps). Secondly, the central column of k-space (kx = 0) coincides with the peak of the MR echo.

How do you get pictures from k-space data?

To go from a k-space data to an image requires using a 2D inverse Fourier Transform. The readout MR signal is a mix of RF waves with different amplitudes, frequencies and phases, containing spatial information. This signal is digitized and raw data are written into a data matrix called K-space.