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Denoising is a fundamental challenge in scientific imaging. Deep convolutional neural networks (CNNs) provide the current state of the art in denoising natural images, where they produce impressive results. However, their potential has barely been explored in the context of scientific imaging. Denoising CNNs are typically trained on real natural images artificially corrupted with simulated noise. In contrast, in scientific applications, noiseless ground-truth images are usually not available. To address this issue, we propose a simulation-based denoising (SBD) framework, in which CNNs are trained on simulated images. We test the framework on data obtained from transmission electron microscopy (TEM), an imaging technique with widespread applications in material science, biology, and medicine. SBD outperforms existing techniques by a wide margin on a simulated benchmark dataset, as well as on real data. Apart from the denoised images, SBD generates likelihood maps to visualize the agreement between the structure of the denoised image and the observed data. Our results reveal shortcomings of state-of-the-art denoising architectures, such as their small field-of-view: substantially increasing the field-of-view of the CNNs allows them to exploit non-local periodic patterns in the data, which is crucial at high noise levels. In addition, we analyze the generalization capability of SBD, demonstrating that the trained networks are robust to variations of imaging parameters and of the underlying signal structure. Finally, we release the first publicly available benchmark dataset of TEM images, containing 18,000 examples.