# Presentations

PO-GePV-I-32 (Sunday, 7/10/2022)   [Eastern Time (GMT-4)]

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Purpose: To discuss the effects of integer truncation on noise calculations in low noise MR images, and present simple correction factors.

Methods: Three common methods to estimate the true standard deviation of the noise (σ) in MR magnitude images use either the standard deviation (SD), mean, or root mean squared (RMS) values of background pixels. Estimates of σ were calculated using each method on Monte Carlo simulations of background noise with σ ranging from 0.1 to 20, using truncation to convert from floating point to integer and assuming RF coils with 1 to18 channels. An exact correction factor was mathematically derived for the mean method and numerically determined using curve fitting for the other methods. Simulations were then verified by acquiring images with a Siemens Body18 coil varying slice thicknesses and BWs to yield mean noise values ranging from 0.4 to 6.7.

Results: The S.D. method overestimates σ by 19% when σ=0.7 and rapidly converges to <1% when σ>3.0. The Mean and RMS methods underestimate σ by 60% to 12% over those same ranges and still exceed 5% when σ=8.0. Once the σ>0.7, the error when using the mean method drops to 0% by simply adding 0.5 to the measured value of the mean noise regardless of the number of channels. Correcting the estimate of σ using either the S.D. or RMS method required fitting the simulations to non-linear equations and were significantly affected by the number of channels. In experimental data, the corrected estimates of σ all converged to within 0.6% of each other regardless of the noise level or number of channels.

Conclusion: Integer truncation causes significant errors in noise estimates in low noise images. It is possible to correct for these errors, the simplest method is to add 0.5 to the mean of the background noise.

Funding Support, Disclosures, and Conflict of Interest: Simply Physics is in the business of providing MRI Quality Control and ACR accreditation services. All of the data presented here were obtained as part of annual MRI performance evaluations.

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