PPG-based heart rate estimation has been widely adopted in wrist-worn devices. However, the motion artifacts caused by the user's physical activities make it difficult to get the accurate HR estimation from contaminated PPG signals. Although many signal processing methods have been proposed to address this challenge, they are often highly optimized for specific scenarios (e.g., running or biking), making them impractical in real-world settings where a user may perform a wide range of physical activities. In this paper, we propose DeepHeart, a new HR estimation approach that features deep-learning-based denoising and spectrum-analysis-based calibration. DeepHeart generates clean PPG signals from ECG signals based on a training data set. Then a denoising convolutional neural network (DnCNN) is trained with the contaminated PPG signals and their corresponding clean PPG signals. Contaminated PPG signals are then denoised by the DnCNN and a spectrum-analysis-based calibration is performed to estimate the final HR. We evaluate DeepHeart on the IEEE Signal Processing Cup (SPC) training data set with 12 records collected during various physical activities. DeepHeart achieves an average absolute error of 1.98 bpm, outperforming two state-of-the-art methods TROIKA and Deep PPG.