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Due to the long imaging times in SPECT, patient motion is inevitable and constitutes a serious problem for any reconstruction algorithm. The measured inconsistent projection data lead to reconstruction artifacts which can significantly affect the diagnostic accuracy of SPECT if not corrected. To address this problem a new approach for motion correction is introduced. It is purely based on the measured SPECT data and therefore belongs to the data-driven motion correction algorithm class. However, it does overcome some of the shortcomings of conventional methods. This is mainly due to the innovative idea to combine reconstruction and motion correction in one optimization problem. The scheme allows for the correction of abrupt and gradual patient motion. To demonstrate the performance of the proposed scheme extensive 3D tests with numerical phantoms for 3D rigid motion are presented. In addition, a test with real patient data is shown. Each test shows an impressive improvement of the quality of the reconstructed image. In this note, only rigid movements are considered. The extension to non-linear motion, as for example breathing or cardiac motion, is straightforward and will be investigated in a forthcoming paper.