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Ultrasonic imaging algorithms used in many clinical and industrial applications consist of three steps: A data preprocessing, an image formation and an image post-processing step. For efficiency, image formation often relies on an approximation of the underlying wave physics. A prominent example is the Delay-And-Sum (DAS) algorithm used in reflectivity-based ultrasonic imaging. Recently, deep neural networks (DNNs) are being used for the data pre-processing and the image postprocessing steps separately. In this work, we propose a novel deep learning architecture that integrates all three steps to enable endto- end training. We examine turning the DAS image formation method into a network layer that connects data pre-processing layers with image post-processing layers that perform segmentation. We demonstrate that this integrated approach clearly outperforms sequential approaches that are trained separately. While network training and evaluation is performed only on simulated data, we also showcase the potential of our approach on real data from a non-destructive testing scenario. Index Terms—deep learning, end-to-end training, Delay-And- Sum, fast ultrasonic imaging, approximate inversion.