During a Single Photon Emitted Computed Tomography (SPECT) the distribution of gamma-ray emitting tracers is measured using detectors which rotate stepwise around the longitudinal axis of the patient. Limited-angle acquisition occurs if not a full 360° rotation is completed and sparse-view, if the step size between each detector position is increased. Both types result in a degradation of the image quality. In this thesis a U-Net architecture, which was already successfully applied to improve the image quality of limited-angle Computed Tomography, was tested on sparse-view SPECT with an angular sampling of 9° and 18° as well as limited-angle SPECT of 240° and 180°. The used data was artificially created with a simulation of different geometric shapes and letters. After the best hyperparameters plus pre- and postprocessing steps had been found (namely the Adam optimizer with a learning rate of 0.001, the perceptual loss function and normalization during preprocessing), the U-Net was trained and tested with the aforementioned different sparse-view and limited-angle problems separately and also in some combinations. Besides a subjective visual evaluation of the image quality the structural similarity index was used as a metric. The U-Net was able to improve the image quality of most sparse-view and limited-angle SPECT images, the exception being the limited-angle SPECT with 240°. Trained in combination with the best performing sparse-view SPECT data of 18° angular sampling, the prediction for the sparse-view datasets with 9° angular sampling and limited-angle with 180°showed improved results. The results suggest, that the U-Net is able to achieve the biggest improvements in the predicted images on the datasets with the biggest underlying artefacts. During the experiments it became apparent, that the U-Net tends to predict additional artefacts in images which mainly depicting the background. The susceptibility of the U-Net regarding certain image structures was also explored by the original authors of the used network [Hua18]. They proposed an additional iterative method to tackle aforementioned problem [Hua19]. Furthermore, investigations with real patient data has to be done to evaluate the possible benefits of deep learning methods on sparse-view and limited-angle SPECT in a clinical setting.