Advances in data-driven deep learning for chest X-ray image analysis underscore the need for explainability, privacy, large datasets and significant computational resources. We frame privacy and explainability as a lossy single-image compression problem to reduce both computational and data requirements without training. For Cardiomegaly detection in chest X-ray images, we propose HeartSpot and four spatial bias priors. HeartSpot priors define how to sample pixels based on domain knowledge from medical literature and from machines. HeartSpot privatizes chest X-ray images by discarding up to 97% of pixels, such as those that reveal the shape of the thoracic cage, bones, small lesions and other sensitive features. HeartSpot priors are ante-hoc explainable and give a human-interpretable image of the preserved spatial features that clearly outlines the heart. HeartSpot offers strong compression, with up to 32x fewer pixels and 11x smaller filesize. Cardiomegaly detectors using HeartSpot are up to 9x faster to train or at least as accurate (up to +.01 AUC ROC) when compared to a baseline DenseNet121. HeartSpot is post-hoc explainable by re-using existing attribution methods without requiring access to the original non-privatized image. In summary, HeartSpot improves speed and accuracy, reduces image size, improves privacy and ensures explainability. Source code: https://www.github.com/adgaudio/HeartSpot