Estimation of Signal and Noise Parameters from MR Data - Advance Image Processing in Magnetic Resonance Imaging - page 132

4.6 CONCLUSIONS

In this chapter, the problem of signal and noise estimation from MR data was
addressed. It was noted that original data coming from the scanner are complex
and Gaussian distributed. However, because of multiple digital-data-processing
steps, the PDF of the resulting data may change. In this chapter, most of the PDFs
one may be confronted with when processing MRI data were discussed along
with their moments and asymptotic behavior.
Furthermore, it was shown how to deal with various PDFs to optimally
estimate signal and noise parameters. Conventional and ML techniques to esti-
mate such parameters were compared. It was shown that methods based on ML
estimation outperform conventional estimators. The ML signal estimator yields
physically relevant solutions for the whole range of SNRs. Also, it was shown
that the ML estimator, unlike conventional signal estimators, cannot be distin-
guished from an unbiased estimator at high SNR.
Finally, the question was addressed as to whether complex or magnitude data
should be used to estimate signal or noise parameters from low SNR data when
using the ML method. In summary, the following conclusions can be drawn:

• The image noise variance should preferentially be estimated from back-

ground data (i.e., from a region of interest in which the true magnitude
values are zero). Thereby, it does not matter whether the noise variance
is estimated from magnitude or complex data.

• On the other hand, whether or not the signal amplitude should be

estimated from magnitude or complex data depends on the underlying
phase values:
•

If the true phase values are known to be constant, the signal ampli-
tude should be estimated from complex-valued data.

• If the true phase values are unknown or if the true phase model

deviates from a constant model, it is generally better, with respect
to the MSE, to estimate the signal amplitude from magnitude data.

4.7 APPENDIX

4.7.1 T RANSFORMATIONS OF PDF S

In image processing, data are often transformed through various arithmetic manipu-
lations. Here, we describe how a PDF changes as a result of such a transformation [54].

4.7.1.1 Theorem

Suppose we wish to determine the PDF, py

y ()

, of y , which is given by

ygx = (), (4.167)