Deep Learning is developing interesting tools which are of great interest for inverse imaging applications. In this work, we consider a medical imaging reconstruction task from subsampled measurements, which is an active research field where Convolutional Neural Networks have already revealed their great potential. However, the commonly used architectures are very deep and, hence, prone to overfitting and unfeasible for clinical usages. Inspired by the ideas of the green-AI literature, we here propose a shallow neural network to perform an efficient Learned Post-Processing on images roughly reconstructed by the filtered backprojection algorithm. The results obtained on images from the training set and on unseen images, using both the non-expensive network and the widely used very deep ResUNet show that the proposed network computes images of comparable or higher quality in about one fourth of time.