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Spatial Frequency
Measure of resolution (lp/mm or lp/cm).
A dimension of the Fourier transformation space (k-space representation of an image), having units of inverse distance. Higher values of spatial frequencies correspond to finer detail in the image.
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Keyhole imaging is used for dynamic imaging with contrast medium. The advantage is that the keyhole technique increases temporal resolution without a loss of spatial resolution by limited data acquisition. Keyhole Fourier imaging updates the low spatial frequencies of the original full, high-resolution data set. The high spatial frequency content of the image is constant in time so that its updating would be unnecessary. The high spatial frequency data is acquired from a baseline image, for example, before injection of a contrast agent.
After contrast injection, only the lower spatial frequency data is acquired because, there is no change in the tissue that is responsible for the higher frequency spatial variation in the image.

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Optimal k-Space Sampling for Dynamic Contrast-Enhanced MRI with an Application to MR Renography
Thursday, 5 November 2009   by    
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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.

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K-space formulation of MRI
Tuesday, 22 March 2005   by    
The Basics of MRI
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Optimal k-Space Sampling for Dynamic Contrast-Enhanced MRI with an Application to MR Renography
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Partial Fourier Technique
The partial Fourier technique is a modification of the Fourier transformation imaging method used in MRI in which the symmetry of the raw data in k-space is used to reduce the data acquisition time by acquiring only a part of k-space data.
The symmetry in k-space is a basic property of Fourier transformation and is called Hermitian symmetry. Thus, for the case of a real valued function g, the data on one half of k-space can be used to generate the data on the other half.
Utilization of this symmetry to reduce the acquisition time depends on whether the MRI problem obeys the assumption made above, i.e. that the function being characterized is real.
The function imaged in MRI is the distribution of transverse magnetization Mxy, which is a vector quantity having a magnitude, and a direction in the transverse plane. A convenient mathematical notation is to use a complex number to denote a vector quantity such as the transverse magnetization, by assigning the x'-component of the magnetization to the real part of the number and the y'-component to the imaginary part. (Sometimes, this mathematical convenience is stretched somewhat, and the magnetization is described as having a real component and an imaginary component. Physically, the x' and y' components of Mxy are equally 'real' in the tangible sense.)
Thus, from the known symmetry properties for the Fourier transformation of a real valued function, if the transverse magnetization is entirely in the x'-component (i.e. the y'-component is zero), then an image can be formed from the data for only half of k-space (ignoring the effects of the imaging gradients, e.g. the readout- and phase encoding gradients).
The conditions under which Hermitian symmetry holds and the corrections that must be applied when the assumption is not strictly obeyed must be considered.
There are a variety of factors that can change the phase of the transverse magnetization:
Off resonance (e.g. chemical shift and magnetic field inhomogeneity cause local phase shifts in gradient echo pulse sequences. This is less of a problem in spin echo pulse sequences.
Flow and motion in the presence of gradients also cause phase shifts.
Effects of the radio frequency RF pulses can also cause phase shifts in the image, especially when different coils are used to transmit and receive.
Only, if one can assume that the phase shifts are slowly varying across the object (i.e. not completely independent in each pixel) significant benefits can still be obtained. To avoid problems due to slowly varying phase shifts in the object, more than one half of k-space must be covered. Thus, both sides of k-space are measured in a low spatial frequency range while at higher frequencies they are measured only on one side. The fully sampled low frequency portion is used to characterize (and correct for) the slowly varying phase shifts.
Several reconstruction algorithms are available to achieve this. The size of the fully sampled region is dependent on the spatial frequency content of the phase shifts. The partial Fourier method can be employed to reduce the number of phase encoding values used and therefore to reduce the scan time. This method is sometimes called half-NEX, 3/4-NEX imaging, etc. (NEX/NSA). The scan time reduction comes at the expense of signal to noise ratio (SNR).
Partial k-space coverage is also useable in the readout direction. To accomplish this, the dephasing gradient in the readout direction is reduced, and the duration of the readout gradient and the data acquisition window are shortened.
This is often used in gradient echo imaging to reduce the echo time (TE). The benefit is at the expense in SNR, although this may be partly offset by the reduced echo time. Partial Fourier imaging should not be used when phase information is eligible, as in phase contrast angiography.
See also acronyms for 'partial Fourier techniques' from different manufacturers.

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Spatial Misregistration ArtifactInfoSheet: - Artifacts - 
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An effect of chemical shift is that of spatial misregistration. Because the frequency displacement caused by chemical shift cannot be differentiated from intended spatial frequency encoding misregistration of the resultant signal may occur along the frequency-encoding direction. This artifact can be seen in a FFE or SE sequence as a bright or dark band at the edge of the anatomy.
See Chemical Shift Artifact.
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