A “stochastic” convolution that describes both image blur and image noise using linear-systems theory

Linear systems theory is widely used to describe the principles of computed tomography (CT), radiography and other medical imaging systems. Using this approach, image blur can be represented as a convolution. However, it is shown that when image blur is a consequence of the spreading of quanta used to represent the image (e.g. X-rays, light or electron-hole pairs), use of the convolution integral underestimates noise in the blurred image. A “stochastic” convolution is introduced which solves this problem by accounting for the statistical properties of the image quanta. It can be used to correctly describe both image blur and image noise within a linear-systems framework