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computerized tomography

In comuterized computerized tomograhy one meaures X-ray images of a body from different angles. Each X-ray image roughly corrsponds to a projection of the density distribution along a certain direction. To obtain the full density distribution inside the body one has to invert the Radon transform. This is an interesting problem from integral geometry which is also challenging concerning the numerical implementation, since the inverse is known the be discontinuous and hence, regularization techniques has to be employed.

Another interesting aspect of this story is that the mathematical problem of the inversion of the Radon transform was done aound 1917 (by Johan Radon itself) while this was totally unknown to the inventors of computerized tomography as it is used today.
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computerized tomography

In comuterized tomograhy one meaures X-ray images of a body from different angles. Each X-ray image roughly corrsponds to a projection of the density distribution along a certain direction. To obtain the full density distribution inside the body one has to invert the Radon transform. This is an interesting problem from integral geometry which is also challenging concerning the numerical implementation, since the inverse is known the be discontinuous and hence, regularization techniques has to be employed.

Another interesting aspect of this story is that the mathematical problem of the inversion of the Radon transform was done aound 1917 (by Johan Radon itself) while this was totally unknown to the inventors of computerized tomography as it is used today.