After reading this chapter, you should be able:

- To explain the relation between time domain, frequency domain and Fourier transform
- To define: spatial frequency, phase and magnitude
- To draw the effects of a point in k-space on the image
- To state the relations between RF pulses, gradients and navigation in k-space
- To describe the k-space trajectory with a spin echo sequence
- To link contrast, spatial resolution and field of view to k-space

- Spatial encoding in MR imaging uses magnetic field gradients. These gradients allow the encoding of spatial data as spatial frequency information. These data are mapped into k-space so that an inverse 2D Fourier transform reconstructs the MR image.

- The location of the data in k-space depends on the strength and the duration of the gradients. If no gradient is applied (or if the net effect of the gradient is null), the location is at the center of k-space. The higher is the net strength of the gradient, or the longer the gradient is applied, the farther from the origin of k-space the data will be located. Gradients are bipolar (negative or positive), so it is possible to move in opposite directions from the center (to the left or the right, and to the top or the bottom).

- Each point of k-space encodes for spatial information of the entire MR image.
- Each point of the MR image is the result of the combination of all the data of k-space.
- The data along a line passing through the center of k-space represent the Fourier transform of the projection of the image onto a line with the same orientation. In other words, a point in k-space encodes for image signal variations in the same direction as the line passing through this point and the center of k-space.

- Center of k-space contains low-spatial-frequency information.
- Most image information is contained in low-spatial-frequency information, corresponding to general shape and contrast.

- Periphery of k-space does not correspond to periphery of the image : it contains high-spatial-frequency information. The higher the spatial frequency, the smaller are the details of the image (edges and spatial resolution).

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