Artifacts are disturbances affecting a measured signal that are not originating from the process itself. This paper addresses the problem of heart rate (HR) monitoring from a photoplethysmography (PPG) sensor, where artifacts caused by body movements affect the quality of the measurement signal. The PPG signal is processed by using the singular spectrum analysis to reduce signal corruption. To remove the artifacts, the artifact-correlated three-dimensional accelerometer signal is used as the auxiliary signal, and a novel spectral subtraction approach is proposed for artifact removal. The cleaned signal is windowed into consecutive time segments, and for each time window of the processed signal and accelerometer data, feature extraction is performed. Ground-truth HR values are obtained from an electrocardiograph sensor during various types of physical activities to capture a broad range of HR variations. A recurrent neural network is used to build a model from extracted features and actual heart rate values to estimate HR from PPG signal.