The X-ray transform is a transform with applications in computed tomography that maps an integrable function to its line integrals.

## Definition

Given a positive integer , and a function , the X-ray transform of is a function defined on the space , by . Here, represents a position in the space for which is defined, whereas represents the direction of the line. Some may restrict the domain of so that , as integration by substitution can show that , if is the (unique) orthogonal projection of onto .