# A Relationship Between Sampling Error And Signal To Noise Ratio In Gated SPECT

J Wheat, G CUrrie

###### Keywords

gated spect, sampling error, signal to noise ratio, snr

###### Citation

J Wheat, G CUrrie. *A Relationship Between Sampling Error And Signal To Noise Ratio In Gated SPECT*. The Internet Journal of Nuclear Medicine. 2006 Volume 4 Number 1.

###### Abstract

Gated SPECT provides temporal resolution at the expense of a deteriorating SNR. While the level of noise in an image data set is thought to be complex due to the filtering process, this article provides a simple method for determining the trade-off in SNR when altering acquisition parameters.

### Introduction

Gated single photon emission computed tomography (SPECT) provides temporal resolution at the expense of a deteriorating signal to noise ratio (SNR) (_{1}). A potential weakness of gated SPECT is the possibility of insufficient count density per individual frame interval despite the relatively high ^{99m} Tc activity (_{2}). Each projection set will be reduced in counts by a factor equal to the number of collected frames (plus any rejected beats) (_{3}). SPECT image quality is adversely affected by noise which is more problematic in low count gated SPECT. Smaller numbers of counts result in larger statistical uncertainties, or noise (_{4}). Radioactivity counting error (random error) is characterised by Poisson statistics (_{4}) which assumes pixels are independent of one another (e.g. planar images and SPECT raw data) and, thus, does not hold for reconstructed SPECT data where reconstructed pixels are not independent.

### Discussion

The level of noise in an image data set, or SNR, is not as intuitive as it might seem due to the filtering process (_{5}). The reconstructed SNR for data reconstructed using a ramp filter can be determined with the following equation:

where N_{R} is the reconstructed counts per pixel and R is the number of pixels (resolution elements) containing activity (_{5}). Thus, using an eight interval gated SPECT, a 64 x 64 matrix, a ramp filter and assuming no beat rejections, the reconstructed SNR will deteriorate by a factor of 2.83 for gated data (over the ungated data).

Sampling error is proportional to the inverse of the square root of the sample size:

When N is reduced by a factor of eight as seen in the total number of events per image in gated SPECT, there is a corresponding increase by a factor of 2.83 in sampling error.

### Conclusion

It is clear that using an eight interval gate increases sampling error and decreases SNR by a factor of 2.83. Furthermore, 2.83 is the square root of eight, thus, we can more simply determine the trade-off in image quality (SNR) and statistical certainty for any number of gate intervals (e.g. using a 16 interval gate would deteriorate SNR and sampling error by a factor of four).

### Correspondence to

Janelle Wheat School of Biomedical Sciences Locked Bag 588 Charles Sturt University Wagga Wagga 2678 Australia Telephone: 61 2 69332750 Facsimile: 61 2 69332866 Email: jwheat@csu.edu.au