Statistical Signal Processing in Engineering

21Tomography

Tomography is the method of getting an inner image of an object by external observations called projections. The word comes from the Greek “tomos,” which means slice, so tomography slices an object from external measurements and gets an image by reconstructing the image from the projections. In radiography diagnostics it is known as computer tomography (CT), and it was investigated by Allan M. Cormack (1963) and later by Godfrey N. Hounsfield (1972), and their research was awarded by the Nobel prize in 1979. CT is a leading diagnostic tool together with magnetic resonance imaging (MRI), which can be considered more complex in terms of imaging method. A lot of progress has been made since the early tomography; the early 2D slices have been enriched by the third dimension to get volumetric (or 3D) CT. The importance of tomographic methods goes beyond diagnostic medical imaging: one can find engineering applications in non‐destructive testing, geoscience imaging, ultrasound imaging, and recently radio imaging. The wide usage of tomographic methods in engineering justifies the discussion here of the basic principles of tomographic imaging methods. An excellent methodological reference is the book by Kak and Slaney [84] , while the basics of the physics of the interaction of radiation with matter is in [85] , or others.

Tomography is based on the measurement of the projections inferred from excitations external to the body. An exemplary CT experiment of X‐ray radiation ...