The photoplethysmographic (PPG) signal is an unobtrusive blood pulsewave measure that has recently gained popularity in the context of the Internet of Things. Even though it is commonly used for heart rate detection, it has been lately employed on multimodal health and wellness monitoring applications. Unfortunately, this signal is prone to motion artifacts, making it almost useless in all situations where a person is not entirely at rest. To overcome this issue, we propose SPARE, a spectral peak recovery algorithm for PPG signals pulsewave reconstruction. Our solution exploits the local semiperiodicity of the pulsewave signal, together with the information about the cardiac rhythm provided by an available simultaneous ECG, to reconstruct its full waveform, even when affected by strong artifacts. The developed algorithm builds on state-of-the-art signal decomposition methods, and integrates novel techniques for signal reconstruction. Experimental results are reported both in the case of PPG signals acquired during physical activity and at rest, but corrupted in a systematic way by synthetic noise. The full PPG waveform reconstruction enables the identification of several health-related features from the signal, showing an improvement of up to 65% in the detection of different biomarkers from PPG signals affected by noise.