Abstract: The present invention is directed to a limited angle tomography in combination with a filtered back projection using a special filter operator X. The filter operator X used within the present invention makes it possible to perform region of interest reconstructions although delivering high quality reconstruction images as generated by high effort SART methods. The used filter operator is purely and solely mathematically determined and defined by the spatial geometry which is used for the limited angle tomography. Without having the need to perform several iterations, the present invention directly calculates a solution, i.e. reconstructed image, equivalent to known iteratively construction methods. Although, incomplete projection data p may only be used, the present invention provides for a high image quality.

Abstract: The present invention is directed to a limited angle tomography in combination with a filtered back projection using a special filter operator X. The filter operator X used within the present invention makes it possible to perform region of interest reconstructions although delivering high quality reconstruction images as generated by high effort SART methods. The used filter operator is purely and solely mathematically determined and defined by the spatial geometry which is used for the limited angle tomography. Without having the need to perform several iterations, the present invention directly calculates a solution, i.e. reconstructed image, equivalent to known iteratively construction methods. Although, incomplete projection data p may only be used, the present invention provides for a high image quality.