The small animal PET scanner ClearPET®Neuro, developed at the Forschungszentrum Julich GmbH in cooperation with the Crystal Clear Collaboration (CERN), represents scanners with an unconventional geometry: due to axial and transaxial detector gaps ClearPet®Neuro delivers inhomogeneous sinograms with missing data. When filtered backprojection (FBP) or Fourier rebinning (FORE) are applied, strong geometrical artifacts appear in the images. In this contribution we present a method that takes the geometrical sensitivity into account and converts the measured sinograms into homogeneous and complete data. By this means artifactfree images are achieved using FBP or FORE. Besides an advantageous measurement setup that reduces inhomogeneities and data gaps in the sinograms, a modification of the measured sinograms is necessary. This modification includes two steps: a geometrical normalization and corrections for missing data. To normalize the measured sinograms, computed sinograms are used that describe the geometrical sensitivity for a given measurement setup. Corrections for the data gaps are achieved by a provisional reconstruction followed by a forward projection of the image. The modified sinograms are homogeneous and complete. Modification of the sinograms and reconstruction with FBP or FORE lead to images without geometrical artifacts and still cost less computation time than using iterative reconstruction algorithms