In a Gaussian filter, what diameter corresponds to an average resolution?

In the context of image processing and specifically within the framework of a Gaussian filter used in tasks such as noise reduction or image smoothing in Positron Emission Tomography (PET), the choice of filter diameter is crucial to defining the average resolution.

A diameter in the range of 7-10mm corresponds to an average spatial resolution because it strikes a balance between reducing noise and preserving the details of the image. A Gaussian filter essentially works by applying weights to nearby pixels, where pixels closer to the center receive higher weights than those further away. This smoothing effect naturally leads to a reduction in high-frequency components, which are often associated with noise.

In PET imaging, clarity and quality of images are paramount for accurate interpretation and diagnosis. A resolution of 7-10mm is often deemed optimal because it diminishes the noise while maintaining sufficient detail in the structures being visualized, which is vital for detecting lesions or abnormalities.

The options surrounding this range, such as those that suggest smaller diameters or larger diameters, would either lead to excessive detail loss (in the case of smaller diameters) or blurring of important structures (in the case of larger diameters). Therefore, the selection of the 7-10mm range is foundational in achieving