rückprojiziert

Rückprojiziert is the past participle of the German verb rückprojekizieren, meaning to back-project. In technical contexts it describes an operation in which measured data are re-mapped into an image or reconstruction space along the lines or rays from which they were originally acquired.

In tomographic imaging, backprojection is the inverse operation of forward projection. Projection data pθ(s) are obtained for various angles θ. Backprojection distributes each measured value along the corresponding line s = x cos θ + y sin θ in the image domain and aggregates contributions from all angles. The result of unfiltered backprojection is typically a blurred version of the original object, due to the geometric spread of contributions.

Because of this blur, backprojection is usually combined with a filtering step, producing filtered backprojection (FBP). In FBP, a high-pass filter is applied to the projection data (often in the frequency domain) before the backprojection step to restore image sharpness and reduce artifacts.

Rückprojektion is a core concept in computed tomography (CT) and in nuclear medicine techniques such as single-photon emission computed tomography (SPECT) and positron emission tomography (PET). It also appears in related computer vision tasks that involve reprojecting 3D information into 2D image spaces.

Etymology and usage: the term reflects the idea of "projecting back" the measured information into the spatial domain. In German-speaking literature, rückprojiziert or die Rückprojektion is used to refer to the operation itself or to images/data produced by it.