We introduce a new method to reconstruct motion and noise artifact (MNA) contaminated photoplethysmogram (PPG) data. A method to detect MNA corrupted data is provided in a companion paper. Our reconstruction algorithm is based on an iterative motion artifact removal (IMAR) approach, which utilizes the singular spectral analysis algorithm to remove MNA artifacts so that the most accurate estimates of uncorrupted heart rates (HRs) and arterial oxygen saturation (SpO2) values recorded by a pulse oximeter can be derived. Using both computer simulations and three different experimental data sets, we show that the proposed IMAR approach can reliably reconstruct MNA corrupted data segments, as the estimated HR and SpO2 values do not significantly deviate from the uncorrupted reference measurements. Comparison of the accuracy of reconstruction of the MNA corrupted data segments between our IMAR approach and the time-domain independent component analysis (TD-ICA) is made for all data sets as the latter method has been shown to provide good performance. For simulated data, there were no significant differences in the reconstructed HR and SpO2 values starting from 10 dB down to -15 dB for both white and colored noise contaminated PPG data using IMAR; for TD-ICA, significant differences were observed starting at 10 dB. Two experimental PPG data sets were created with contrived MNA by having subjects perform random forehead and rapid side-to-side finger movements show that; the performance of the IMAR approach on these data sets was quite accurate as non-significant differences in the reconstructed HR and SpO2 were found compared to non-contaminated reference values, in most subjects. In comparison, the accuracy of the TD-ICA was poor as there were significant differences in reconstructed HR and SpO2 values in most subjects. For non-contrived MNA corrupted PPG data, which were collected with subjects performing walking and stair climbing tasks, the IMAR significantly outperformed TD-ICA as the former method provided HR and SpO2 values that were non-significantly different than MNA free reference values.