K-space

The imaging "trick" in MR is that different spatial positions are mapped into different MR resonance frequencies (frequency encoding, phase encoding) (Fig.1: x®w). Rather than recording individual resonance frequencies, the MR scanner records time dependent radiofrequency bursts (w®t), data which are related to the frequency domain data by an inverse Fourier transformation. Just as the spatial positions can be mapped into frequencies, temporal information can be mapped into k-information (t®k). Hence, MR is said to acquire data in k-space. A Fourier transformation will convert k-space data to image data (k®x). Because an image is at least a 2D space, we speak of k-space which is a plane for 2D MR imaging and a 3D space for 3D MR imaging

It is difficult to gain an intuitive feeling as to how imaging data might look in k-space, but extended image features are imaged into the centre and point-like objects are mapped into extended regions in k-space. This translates into the frequently expressed statement that the contrast of an image is mapped into the centre of k-space while high resolution fine detail structures are represented in its peripheral regions. Hence, k-space has to be mapped extensively to enable the reconstruction of a high resolution image. Like scanning TV-images line by line, k-space can be sampled line by line and a Fourier transform of it will then result in the desired image. Typically in MR imaging, data points in k-space are indeed sampled line by line. In Fig.2 on the left a k-space trajectory is shown for a standard pulse sequence, on the right for an echo planar imaging EPI sequence. Many other strategies, however, have been devised to sample data points in k-space. Data points on each k-space line can be spaced at equal distances (linear sampling) or at variable distances (nonlinear sampling). The best known strategies in use, not following the schemes indicated in Fig. 2, are interleaved echo-planar imaging (see echo-planar imaging (EPI) (I), Fig. 2) , the mosaic technique and spiral scanning characterized by a spiral k-space trajectory (spiral scanning (I), Fig. 1). In order to optimize image acquisition, strategies have also been devised to sample only fractions of k-space such as in partial Fourier technique. More frequent sampling of the central k-space region than the periphery will provide rapid update of contrast changes in an image, i.e. after injection of contrast media, but less frequent updates of subtle high resolution changes in an image (keyhole imaging). Finally, limited sampling of k-space may become very useful in instrument visualization in interventional MR imaging.

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