Background

Tomography

Projections of Bob, our little plastic patient.

Tomography is a technique for creating three-dimensional images of objects without taking them apart. Instead of making the image directly, it is computed from a series of projection images, recorded while viewing the object from a range of angles.

The most common example of tomography can be found in a medical CT-scanner. An assembly, consisting of an X-ray source and an X-ray detector, rotate around the patient, while acquiring X-ray photos from a full range of angles. This movie illustrates how a full CT-scan is made of a simulation patient (actually, a toy figure) in a micro-CT scanner. After recording all the X-ray photos, the series of images is then used as input for a reconstruction algorithm. The reconstruction algorithm computes a three-dimensional image of the internal organs of the patient, based on the two-dimensional projection images (the X-ray photos). When the 3D volume has been computed, it can be visualized in various ways. It is now possible to display slices through the patient's body, or display a 3D volume rendering.

Traditional reconstruction

Volume rendering of Bob, our little plastic patient.Traditional reconstruction methods that are used in nearly all practical applications of tomography, such as the Filtered Backprojection method, are capable of computing accurate reconstructions quite fast. However, they require a large number of X-ray photos (many viewing angles), and a full 180 degree rotation. If few photos are available, or only from a limited angular range, they perform badly. Making many X-ray photos usually means a longer scanning time. In some applications of tomography, mainly in industry and science, it is not even possible to record many images.

Prior knowledge

In practice, we often have certain knowledge about the patient, or object, that has been scanned. For example, our simulation patient Bob is obviously not a real patient, but a toy. Therefore, we can expect his body to consist of plastic and air. If Bob were real, he would mainly consist of blood, bone and soft tissue. Traditional reconstruction methods do not use any of this knowledge at all. At our research group ASTRA, we develop new reconstruction methods that take this type of prior knowledge into account. For example, if we know that Bob consists of plastic, we can reconstruct his body from only a very limited number of X-ray photos, even if his arms stick out of the X-ray photo in some of the views!

Computation time

Our computational methods that incorporate prior knowledge are very powerful, but they also have a major drawback. Computing a full 3D reconstruction, which is already a time-consuming procedure for conventional tomography, requires a huge amount of computation. Reconstructing a full 3D volume consisting of a billion volume elements takes several days, even on our small cluster, consisting of four quad-core PCs. The FASTRA allows us to perform these computations within an hour, which brings our techniques into the realm of real-world application opportunities.

Applications

The most common practical example of tomography can be found in the medical CT-scanner. Less known is the fact that tomography has many important applications outside the field of medical imaging as well. In fact, tomography can be used, and is being used, at all imaginable scales. It reaches from the reconstruction of individual atom positions in nanocrystals at sub-Angstrom resolution, to the determination of galaxy locations in astronomy. The entire spectrum of scales between these two extremes is covered fairly well by a range of other applications. Most research groups that deal with tomographic image reconstruction focus on a specific application domain, such as Medical Imaging or Materials Science. Yet, reconstruction problems at different scales share many common features and can often be solved using similar methods. In the ASTRA research group of the University of Antwerp we target the entire range of tomographic reconstruction problems, at all scales. By focusing on the underlying general mathematical problems, instead of a specific application field, we develop reconstruction methods that can be shared between the various application fields.