What is the formula for calculating Noise Equivalent Count Ratio (NECR)?

The formula for calculating the Noise Equivalent Count Ratio (NECR) is particularly important in the field of Positron Emission Tomography (PET) as it quantifies the quality of the signal against the background noise, allowing for an assessment of the imaging performance. The correct formula is derived from the values representing true counts, scatter counts, and random counts in the imaging process.

In this case, the NECR is calculated by taking the square of the number of true counts (T) because the signal's effectiveness is proportional to the square of the counts collected, reflecting the statistical nature of imaging. This squared term accounts for the increased signal strength as the number of detected true events rises.

The denominator includes the sum of true counts (T), scatter counts (S), and random counts (R). These components represent the overall count of events detected by the system, which also incorporates the undesirable noise that affects image quality. By dividing T squared by this sum, the NECR effectively gives a ratio that indicates how much of the signal is 'useful' (true counts) compared to the 'noise' (scatter and random counts).

This ratio is crucial because a higher NECR value indicates a better signal-to-noise ratio, leading to improved image