To construct an MR image, the scanner must receive the MR signal that is emitted by the tissue. This is accomplished using an RF coil that is designed to magnetically couple to the tissue of interest. The MR signal is Òpicked upÓ by the receiving RF coil as an induced voltage. This voltage is amplified and converted to a digital signal (i.e. a number) by an Analog-to-Digital converter (A/D). This A/D converter samples the analog voltage at a rate defined by the user (receive bandwidth, or RBW). Higher RBW, or sampling rates, require shorter sampling times for each data point. For example, sampling at RBW = 31.25 kHz requires that a complex data pair is acquired every 16 ms, whereas sampling at RBW = 62.5 kHz requires the acquisition of a complex data pair every 8 µs.* Acquisition of 256 data points at RBW = 31.25 kHz results in an acquisition window of 4.1 ms, whereas 256 data points can be acquired at RBW = 62.5 kHz in half the time.

Because the noise on the MR signal is random in time, sampling the signal for longer (i.e. the A/D "listens" to the signal for a longer time) results in a more precise measure of the signal. This means that the certainty that can be associated with a particular measured signal intensity is higher. The signal is increased relative to the noise level, i.e. the SNR is increased for longer sampling times. In the example given above, the acquisition window for 256 data points is twice as long with RBW = 31.25 kHz compared to RBW = 62.5 kHz. The SNR is therefore higher for the acquisition with the narrower bandwidth. In general, the rule for SNR dependence on sampling time is that the SNR increases as the square root of the total time for which the signal is sampled. This dependency of SNR on sampling time combined with its dependency on voxel size can be expressed using a simple equation:

(1.1)

where gives the tissue voxel size, n_x and n_y give the acquisition matrix size in the readout (XRES) and phase directions (YRES) respectively, and is the sampling time for a data pair. NEX is the number of signal averages, or excitations. Figure 1.3 illustrates the dependence of SNR on voxel size with the total sampling time held constant. With the total sampling time set equal by varying the RBW and the NEX, the SNR is doubled for the 256 x 128 acquisition compared to the 256 x 256 matrix size.

Figure 1.3 Images of a GE quality assurance phantom acquired using: (A) matrix size=256 x 256, RBW=32kHz, slice thickness=10mm, 1NEX; (B) matrix size=256 x 128, RBW=16kHz, slice thickness=10mm, 2NEX.

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*In GE terminology, the RBW is given as the half-bandwidth (i.e. the maximum frequency) as opposed to the full-bandwidth (which is actually +/- 31.25kHz). The MR data is a complex-pair (it is still real data, but has an x- and y-component, so the complex formalism is mathematically convenient), so we actually acquire a complex-pair at a rate of 62.5kHz for RBW=31.25kHz.