Figure 12

Image reconstruction, k-space and image space. The MR signals derived from each phase encoding step are stored in a raw data matrix, known as k-space. A two-dimensional Fourier transformation of this matrix results in the reconstruction of the image. The number of phase encoding steps determines the number of pixels in the image along the phase encoding direction. The coordinates of the image are the spatial coordinates x and y. The distribution of MR signal components in the image is determined by their frequency along the frequency encoding direction (in this case, x) and by their change in phase with each phase encoding step along the phase encoding direction (in this case, y). The Coordinates of k-space are the spatial frequencies k_x = 1/x and k_y = 1/y. The data points in k-space (the sampled MR signals) therefore represent the spatial frequencies content of the image. In a Cartesian data acquisition, the data points are stored line by line along the k_x direction, with each line corresponding to a separately sampled MR signal. The position along k_x depends on the time point during the sampling period. The location of each line of data points in the k_y direction is determined by the amplitude and duration of the phase encoding direction at each phase encoding step.