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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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Further Reading:
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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K-Space Trajectory
The path traced in the spatial-frequency domain during data collection as determined by the applied gradients.

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Spiral K-Space Coverage
Acquisition of data whose views cover a spiral in k-space. It is accomplished by applying an oscillatory gradient, which increases in amplitude as a function of time.
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Interleaved K-Space Coverage
The sequential collection of raw data from multiple excitations such that each excitation samples multiple lines or curvilinear paths in k-space.
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Segmented K-Space Data Acquisition
A set of k-space lines collected in a specified order but not constituting a complete coverage of k-space, thus can be used in conjunction with all ultrafast MRI techniques. Several segmental acquisitions may need to be run for complete coverage of k-space. If these lines are recorded for a single rather than multiple images, imaging time can be shortened considerably maintaining an acceptable temporal resolution.
For example, rapidly acquiring eight k-space lines per segment after each trigger until 128 lines of k-space are acquired in 16 triggers, thus makes image acquisition of multiple cardiac phases or anatomical slices possible in a breath-hold.
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