Table 1 Performance of the estimation pipeline and heterogeneity stains evaluated using different signal-to-noise ratio (SNR) for three different DTDs.

From: A new framework for MR diffusion tensor distribution

DTD type

SNR

Estimation error in mean tensor (%)

Estimation error in covariance tensor (%)

Error in \(\text {V}_{\text {size}}\) (%)

Error in \(\text {V}_{\text {shape}}\) (%)

Error in \(\text {V}_{\text {orient}}\) (%)

Size heterogeneity

5

4.0

30.0

14.9

–

–

10

4.0

30.0

14.9

–

–

20

1.0

5.0

2.1

–

–

\(\infty\)

2.0

10.0

6.4

–

–

Shape heterogeneity

5

2.0

60.0

–

40.0

–

10

1.0

50.0

–

40.0

–

20

1.0

30.0

–

17.5

–

\(\infty\)

0.6

30.0

–

15.0

–

Orientation heterogeneity

5

1.0

30.0

–

–

24.1

10

0.8

20.0

–

–

20.7

20

0.8

20.0

–

–

20.7

\(\infty\)

0.8

20.0

–

–

20.7

  1. Size heterogeneity refers to isotropic emulsion type DTD, shape heterogeneity refers to shape heterogeneous DTD with isotropic mean diffusion tensor and orientation heterogeneity refers to the DTD with two fibers crossing at 90\(^\circ\). The estimation error in mean and covariance tensors are calculated using the Frobenius norm of the difference between the actual and estimated tensors divided that of the actual tensor and expressed as percentage. The error in stains (i.e. \(\text {V}_{\text {size}},\text {V}_{\text {shape}}, \text {and}~\text {V}_{\text {orient}}\)) were expressed as percent change from the ground truth value.
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