Measurement Reduction Methods for Processing Tomographic Images.

The importance of development of new methods for reconstruction of an object image given its sinogram and some additional information about the object stems from the possibility of artifact presence in the reconstructed image, or its insufficient sharpness when the used additional information does not hold. The problem of recovering artifact-free images of the studied object from tomography data is considered in the framework of the theory of computer-aided measuring systems. Methods for solving it are developed. They are based on narrowing the class of possible images using less artifact-inducing information. An example of such information is the natural condition of non-negativeness of the estimated brightnesses. The main problem that arises is the large dimensionality of the images, which prevents the use of direct algorithms. One proposed method is based on local approach, namely correction of the result of unfiltered backprojection by applying a locally (in the space of the output image) optimal linear transformation. Another method processes a sinogram directly, without using backprojection, using iterative implementation of the measurement reduction technique. Examples of use of the proposed methods for processing teeth sinograms are given.