Tomographic gamma scanning (TGS) is a nondestructive testing (NDT) method commonly used for radioactive waste. Traditional transmission image reconstruction algorithm require the projection data to match the line integral value of the reconstructed image in the corresponding projection direction, and use a single detector for scanning, resulting in cumbersome and time-consuming scanning processes that severely limit the industrial application of TGS. Sparse angular scanning can effectively improve the efficiency of TGS systems. However, the amount of data generated by sparse angular scanning can make it difficult to support traditional algorithms, resulting in blurry artifacts in the reconstructed image. This work utilizes array detectors to achieve fast and high-precision reconstruction for TGS transmission images under sparse angular scanning, based on the Algebraic Reconstruction Technique (ART) and a new residual network (ResNeXt). Geant4 simulation and a self-developed TGS device with array detectors were used for both simulation experiments and real experiments to verify the proposed method. The proposed method was compared to other algorithms, including ART, ART-NLM, ART-TV, and ART-DenseNet, using two metrics, MSE and SSIM, for evaluation. The experimental results show that the average MSE of ResNeXt is 56.3%, 26.5%, 24.4%, and 8.4% lower than ART, ART-NLM, ART-TV, and DenseNet, respectively. The SSIM averages are 36.4%, 14.8%, 15.3%, and 4.8% higher than ART, ART-NLM, ART-TV, and DenseNet, respectively. It can be concluded that when using the same sparse projection data, the improved ART-ResNeXt reconstruction methods generate TGS transmission images with better reconstruction quality and faster reconstruction speed compared to reconstruction methods like ART, ART-NLM, ART-TV and ART-DenseNet. The improved ResNeXt exhibits significant adaptability. Even when encountering gamma ray energy and medium types that are not present in the neural network training set, the reconstruction process achieves the highest quality while maintaining the fastest speed possible.