Signal-to-noise measurements in magnitude images from NMR phased arrays

Abstract

A method is proposed to estimate signal-to-noise ratio (SNR) values in phased array magnitude images, based on a region-of-interest (ROI) analysis. It is shown that the SNR can be found by correcting the measured signal intensity for the noise bias effects and by evaluating the noise variance as the mean square value of all the pixel intensities in a chosen background ROI, divided by twice the number of receivers used. Estimated SNR values are shown to vary spatially within a bound of 20% with respect to the true SNR values as a result of noise correlations between receivers.

FIG. 1

The chi distribution of M_n/σ for several values of A_n/σ for a (a) single-receiver system, (b) two-receiver system, and (c) four-receiver system.

FIG. 2

(a) The measured SNR $({\stackrel{-}{M}}_n∕\sigma )$ and (b) the normalized standard deviation (σ_Mn/σ) plots for a magnitude sum-of-squares image obtained using single-, two-, and four-receiver systems, for several values of A_n/σ, in a uniform region of the image.

FIG. 3

Correction plots in sum-of-squares magnitude images for single-, two-, and four-receiver systems as a function of ${\stackrel{-}{M}}_n∕\sigma$ Corrected SNR values were obtained by subtracting the appropriate correction factor from ${\stackrel{-}{M}}_n∕\sigma$.

FIG. 4

(a), (b) Midaxial and midcoronal images of a cylindrical water phantom generated by dividing the calculated SNR values by the true SNR values in the case of a (a) two-receiver and a (b) four-receiver system. The background intensities in both images were suppressed using a thresholding algorithm. (c), (d) Profiles taken along the midline of each of the images in (a) and (b) above.