We propose a novel convolutional neural network for lesion detection from weak labels. Only a single, global label per image - the lesion count - is needed for training. We train a regression network with a fully convolutional architecture combined with a global pooling layer to aggregate the 3D output into a scalar indicating the lesion count. When testing on unseen images, we first run the network to estimate the number of lesions. Then we remove the global pooling layer to compute

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... n maps of the size of the input image. We evaluate the proposed network on the detection of enlarged perivascular spaces in the basal ganglia in MRI. Our method achieves a sensitivity of 62% with on average 1.5 false positives per image. Compared with four other approaches based on intensity thresholding, saliency and class maps, our method has a 20% higher sensitivity.