Chest radiographs are commonly performed low-cost exams for screening and diagnosis. However, radiographs are 2D representations of 3D structures causing considerable clutter impeding visual inspection and automated image analysis. Here, we propose a Fully Convolutional Network to suppress, for a specific task, undesired visual structure from radiographs while retaining the relevant image information such as lung-parenchyma. The proposed algorithm creates reconstructed radiographs and ground-truth data from high resolution CT-scans. Results show that removing visual variation that is irrelevant for a classification task improves the performance of a classifier when only limited training data are available. This is particularly relevant because a low number of ground-truth cases is common in medical imaging.