This study aims to develop an accurate framework for respiratory rate (RR) monitoring from the photoplethysmogram (PPG). Sparse signal reconstruction (SSR) is used to obtain a sparse representation of the PPG signal in the spectral domain. Based on the assumption that the RR from two highly overlapped consecutive windows does not change much, RR tracking (RRT) then selects the most appropriate frequency component based on the previous RR. It also produces a signal quality index to determine whether or not to report the RR estimate for a given window. The results were validated on a public benchmark database, Capnobase. Our approach outperforms a state-of-the-art algorithm in the number of RR estimates and accuracy and achieves an overall root mean squared error (RMSE) of 3.25 breaths min(-1), an overall mean absolute error (MAE) of 0.95 breaths min(-1), and an overall mean absolute percentage error (MAPE) of 7.13%. In conclusion, we have proposed a novel framework that can accurately monitor RR from the PPG via SSR. This is the first time SSR has been used in RR monitoring from the PPG. Unlike existing methods which require a high sampling frequency, our approach works well when the PPG signal is sampled at 10 Hz, making it potentially useful in low-cost wearable devices.