Computed Tomography

Tomographic reconstruction is a type of inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. One of the coolest parts of this process is the fourier slice theorem: the 1D Fourier Transform of the projection of an object at angle $\Theta$ is equal to the slice of the 2D Fourier Transform of the object at angle $\Theta$. Using this, we can take multiple projections to construct the 2D Fourier Transform of the object, and then take its inverse to get the original object.

Example