Assessment of averaging spatially correlated noise for 3-D radial imaging

Any measurement of signal intensity obtained from an image will be corrupted by noise. If the measurement is from one voxel, an error bound associated with noise can be assigned if the standard deviation of noise in the image is known. If voxels are averaged together within a region of interest (ROI) and the image noise is uncorrelated, the error bound associated with noise will be reduced in proportion to the square root of the number of voxels in the ROI. However, when 3-D-radial images are created the image noise will be spatially correlated. In this paper, an equation is derived and verified with simulated noise for the computation of noise averaging when image noise is correlated, facilitating the assessment of noise characteristics for different 3-D-radial imaging methodologies. It is already known that if the radial evolution of projections are altered such that constant sampling density is produced in k-space, the signal-to-noise ratio (SNR) inefficiency of standard radial imaging (SR) can effectively be eliminated (assuming a uniform transfer function is desired). However, it is shown in this paper that the low-frequency noise power reduction of SR will produce beneficial (anti-) correlation of noise and enhanced noise averaging characteristics. If an ROI contains only one voxel a radial evolution altered uniform k-space sampling technique such as twisted projection imaging (TPI) will produce an error bound ~35% less with respect to noise than SR, however, for an ROI containing 16 voxels the SR methodology will facilitate an error bound ~20% less than TPI. If a filtering transfer function is desired, it is shown that designing sampling density to create the filter shape has both SNR and noise correlation advantages over sampling k-space uniformly. In this context SR is also beneficial. Two sets of 48 images produced from a saline phantom with sodium MRI at 4.7T are used to experimentally measure noise averaging characteristics of radial imaging and good agreement with theory is obtained.