A theoretical framework for filtered backprojection in tomosynthesis

Tomosynthesis provides only incomplete 3D-data of the imaged object. Therefore it is important for reconstruction tasks to take all available information carefully into account. We are focusing on geometrical aspects of the scan process which can be incorporated into reconstruction algorithms by filtered backprojection methods. Our goal is a systematic approach to filter design. A unified theory of tomosynthesis is derived in the context of linear system theory, and a general four-step filter design concept is presented. Since the effects of filtering are understandable in this context, a methodical formulation of filter functions is possible in order to optimize image quality regarding the specific requirements of any application. By variation of filter parameters the slice thickness and the spatial resolution can easily be adjusted. The proposed general concept of filter design is exemplarily discussed for circular scanning but is valid for any specific scan geometry. The inherent limitations of tomosynthesis are pointed out and strategies for reducing the effects of incomplete sampling are developed. Results of a dental application show a striking improvement in image quality.