Based on the success of deep neural networks for image recovery, we propose a new paradigm for the compression and decompression of ultrasound~(US) signals which relies on stacked denoising autoencoders. The first layer of the network is used to compress the signals and the remaining layers perform the reconstruction. We train the network on simulated US signals and evaluate its quality on images of the publicly available PICMUS dataset. We demonstrate that such a simple architecture outperforms state-of-the art methods, based on the compressed sensing framework, both in terms of image quality and computational complexity.