This book constitutes the refereed proceedings of the 4th International Workshop on Simulation and Synthesis in Medical Imaging, SASHIMI 2019, held in conjunction with MICCAI 2019, in Shenzhen, China, in October 2019.The 16 full papers presented were carefully reviewed and selected from 21 submissions. The contributions span the following broad categories in alignment with the initial call-for-papers: methods based on generative models or adversarial learning for MRI/CT/PET/microscopy image synthesis, image super resolution, and several applications of image synthesis and simulation for data augmentation, segmentation or lesion detection.