Local reconstruction of tomographic images in parallel and fan-beam scanning schemes

Tomographic methods for reconstructing images of objects are widely used in a variety of fields, including medicine, biology, plasma physics, gas dynamics, geophysics, astronomy, and radar. In some applications, it is impossible (or undesirable) to obtain a complete set of projection data to restore the image of the entire object. Sometimes, only a portion of the image (often small compared to the image of the whole object) is of interest, and the problem of local reconstruction with an incomplete set of projections arises. One of the most popular methods for solving this problem is the wavelet decomposition, which allows local restoration of small image structures. The wavelet decomposition method is applicable for the parallel tomographic scan scheme. In the fan-beam scheme, the projection rearrangement method is usually used, which makes it possible to apply the reconstruction algorithms developed for the parallel scheme. The paper considers the question of changing the required amount of projection data during the transition from the fan-beam to parallel scheme.