Signal‐to‐noise in phase angle reconstruction: Dynamic range extension using phase reference offsets

Abstract

The dynamic range of phase-reconstructed magnetic resonance images is compared to that of magnitude-reconstructed images. From analysis of propagation of errors, the phase angle noise is phase-independent and given in radians by sigma ([I])/[I], the noise-to-signal ratio of the corresponding magnitude-reconstructed image. As the phase can range from minus pi to pi, the phase angle dynamic range is 2 pi times that of the signal magnitude. These results agree with experiment, verifying that the noise in the two receiver channels is uncorrelated. An artifact-free technique is presented for correcting phase spillover, which further extends the phase angle dynamic range. The reconstruction-based reference phase is adjusted on a local basis so that the boundary of phase wraparound is reconstructed near the center of the [- pi, pi] interval. For a particular flow study, the phase signal-to-noise was extended over twofold by spillover correction, to a value 15 times that of the magnitude signal-to-noise.

Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results

“…In this step, all the noiseless signal was placed in the real channel, as allowed because of the phase independence of magnitude-reconstructed noise as suggested 64 and derived. 71 Finally, independent noise fluctuations were added to M copies of the noiseless DT-MRI data to generate M frames of noisy DT-MRI images, which were then averaged to simulate the DTT experiment (M = 10 for the standard case).…”

“…The behavior of g as a function of r and i was simulated 44 assuming that e r and e i are independent and uncorrelated, as is the case for MR thermal noise. 71 These simulations determined that g decreases from 0.786 as r and i deviate from equality, so that g can be used to verify that r = i in the magnitude DT-MRI data.…”

“…71 This high angular precision is coupled with the small voxel size and step size to lead to very small errors in a given track step. As an example, for an eigenvector directional error of 1°, the random error in a step from one voxel to the next would be 40 mm.…”

“…Accordingly, we assume that r = i = 1 , as was observed in conventional MRI. 71 From measurement of hI 2 obs i ROI 2 2 1 , the intrinsic noise in the 1-frame I 0 image is 1 = 21.7 AE 2.2. The same intrinsic noise level was assumed for all seven DWIs because diffusion weighting is not expected to change the random thermal noise.…”

Real‐time geometric distortion correction for interventional imaging with echo‐planar imaging (EPI)

“…Conturo et al (14) have demonstrated that the phase error is inversely proportional to the signal-to-noise ratio (SNR) of the complex MR image, i.e. ( ) ϭ (|I|)/|I| ϭ 1/SNR, where I and (|I|) represent the intensity and the noise level of the magnitude image, respectively.…”