When selecting the matrix size on a Signa scanner, the user is limited to discrete choices. Both the X-resolution (Xres) and Y-resolution (Yres), (i.e. the numbers of frequency encoding and phase encoding steps respectively) are user-selectable variables. The allowed values for Xres and Yres are determined by the requirements of the Fast Fourier Transform (FFT) operation that is used by the GE scanner to convert the detected MR signal into an image. This operation demands that the input data contain 2ⁿ data points in each dimension (i.e. x and y). When selecting a value for Xres for example, users are limited mainly to choices of 2 ⁶ = 64, 2 ⁷ = 128, 28 = 256, etc. A limited selection of intermediate values like 224 and 384 are also provided, however, these intermediate values use zero-filling in place of the missing data so that 2ⁿ data points are still available for the FFT. Because the image data is the direct result of the FFT, the image display matrix will always have dimensions equal to 2ⁿ pixels per side.

The operation of zero-filling in place of missing k-space data is the mathematical equivalent of performing a sinc interpolation in the image domain. Figure 1.9 illustrates the principle of zero-filling in k-space, and shows how the missing image data are calculated by sinc interpolation/zero-filling. Zero-filling is also used to display square pixels in an image when unequal values for Xres and Yres are chosen. Square pixels can be created in the reconstructed image from a rectangular acquisition matrix by zero-filling in place of the missing phase encode lines in a square k-space matrix. In-plane ZIP is a further extension of this principle, and allows the user to increase the size of the image display matrix, using zero-filling for the extra missing data to provide an interpolated image. Slice ZIP can also be used with 3D imaging techniques to create an interpolated higher image resolution data set in the z-dimension.

Figure 1.9 Zero-filling in k-space is mathematically equivalent to performing a sinc interpolation in image space, i.e. the image data is calculated by convolving with a sinc function.

Matrix sizes are constrained by the GE Signa to have Xres greater than or equal to Yres. This is a somewhat arbitrary constraint, but reflects the practical fact that the Xres can sometimes be increased without requiring any other modifications to the other timing parameters. An increase in Yres automatically entails an increase in scan time because more phase-encode lines must be collected. Provided that the chosen TE is long enough to allow a longer acquisition window, Xres can be increased without affecting scan time, whereas, increasing the number of phase encodes in a standard imaging sequence necessarily results in an increase in the total scan time for the image. This means that after a particular value of Yres, TE and RBW have been chosen, it may be possible to increase the real spatial resolution of the image in the x-direction by increasing Xres, without suffering any drawback with respect to acquisition time.