Background and Applications

The story of X-ray tomography starts with the invention of X-rays, due to Professor Röntgen. The left image shows Professor Röntgen himself. The picture on the right is one of the first-ever x-ray images, showing his wife's hand. It was taken on December 22, 1895.

Hounsfield and Cormack developed tomographic imaging, based on taking X-ray images of a target from different directions and combining the information cleverly into a three-dimensional reconstruction. Shown on the right is one of the early tomographic images reconstructed by Hounsfield. It shows the cross-section of a human head. The next two slides illustrate the scanning geometry of Hounsfield's device.

This sweeping movement was used in first-generation CT scanners, including those built by Hounsfield.

This is the so-called parallel-beam geometry of tomographic imaging. The combination of X-ray source and detector is rotating around the object, collecting projection data from many directions. The data is organized as columns in the so-called sinogram, namely the image shown on the right.

Actually, Johann Radon had solved the mathematical problem of (two-dimensional) X-ray tomography already in 1917. However, it took a long time before this theoretical breakthrough was used in practical imaging. Starting from the 1970's, the tomographic reconstruction algorithm of choice in almost all commercial scanners has been filtered back-projection, based on Radon's formula.

Most commercial Computerized Tomography (CT) scanners use some variant of the Filtered Back-Projection method, which is a computer implementation of Johann Radon's inversion formula. Such methods require dense angular sampling of data to yield high image quality. CT scans are extremely useful for doctors due to the high level of detail in the images, and scanning is a very common practice in modern hospitals. For example, in 2014 almost 5 million CT scans were performed in England [source: COMARE report]. The next slide illustrates filtered back-projection, and the following three slides show some examples of the use of CT images.

Tomographic reconstruction method called filtered back-projection applied to the parallel-beam data collected from the two-dimensional Shepp-Logan phantom (a model of a cross-section of human head).

Medical use of CT scans, example 1 of 3.

Medical use of CT scans, example 2 of 3.

Medical use of CT scans, example 3 of 3.