Real-time pulse rate (PR) monitoring based on photoplethysmography (PPG) has been drawn much attention in recent years. However, PPG signal detected under movement is easily affected by random noises, especially motion artifacts (MA), affecting the accuracy of PR estimation. In this paper, a parallel method structure is proposed, which effectively combines wavelet threshold denoising with recursive least squares (RLS) adaptive filtering to remove interference signals, and uses spectral peak tracking algorithm to estimate real-time PR. Furthermore, we propose a parallel structure RLS adaptive filtering to increase the amplitude of spectral peak associated with PR for PR estimation. This method is evaluated by using the PPG datasets of the 2015 IEEE Signal Processing Cup. Experimental results on the 12 training datasets during subjects' walking or running show that the average absolute error (AAE) is 1.08 beats per minute (BPM) and standard deviation (SD) is 1.45 BPM. In addition, the AAE of PR on the 10 testing datasets during subjects' fast running accompanied with wrist movements can reach 2.90 BPM. Furthermore, the results indicate that the proposed approach keeps high estimation accuracy of PPG signal even with strong MA.

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm is developed to approximate the RLS-based online NMF algorithm with low complexity. The proposed algorithm is evaluated in terms of audio source separation, and the results show that the performance of the proposed algorithms are superior to that of the conventional online NMF algorithm with significantly reduced complexity.