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The dependence of signal-to-noise ratio (SNR) on the analog filter, the sampling rate and the number and dimensions of voxels is derived for magnetic resonance imaging (MRI). It is shown that the object signal-to-noise ratio scales directly with the voxel volume and the square root of the number of voxels. Defining an efficiency figure of merit as the SNR divided by the square root of the imaging time, it is shown that efficiency is always improved when imaging with the lowest possible resolution (largest voxel dimensions) consistent with viewing the desired anatomical detail. The results directly imply the relative efficiency of 3-D (volume), 2-D (plane), 1-D (line) and 0-D (point) imaging techniques. It is shown that spatial averaging is an inefficient method of noise reduction in MRI. As long as voxel size is maintained constant, one can image as many pixels in the readout direction as desired with no loss in SNR; that is, the number of pixels in the readout direction has no effect on the image SNR. Further, multiple sampling of each phase encoding value (to improve SNR) has no advantage over increasing the number of pixels in the phase encoding direction while leaving the voxel size constant. Some experimental observations are given.
Parker et al. (Thu,) studied this question.