The intelligent wearable heart rate measurement requirement has attracted more and more attention, and the related applications of Internet of Things are emerging. However, under intensive physical exercises, motion artifacts are strong interference sources for wrist-type photoplethysmography (PPG) sensor signals, thus significantly affecting the accurate estimation of heart rate and other physiological parameters. Currently, how to effectively remove the motion artifacts from PPG sensor signals is becoming an active and challenging research realm. In this paper, we propose a multi-channel spectral matrix decomposition (MC-SMD) model to accurately estimate heart rate in the presence of intensive physical activities. Motivated by the observation that the PPG signal spectrum and the acceleration spectrum have almost the same spectral peak positions in the frequency domain, we first model the removal of motion artifacts as a spectral matrix decomposition optimization problem. After removing motion artifacts, we propose a new spectral peak tracking method for estimating heart rate. Experimental results on the wellknown PPG data sets recorded from 12 subjects during intensive movements demonstrate that MC-SMD can efficiently remove the motion artifacts and retrieve an accurate heart rate using multi-channel PPG sensor signals.INDEX TERMS Accelerated proximal gradient (APG) method, compressive sensing, heart rate measurement, photoplethysmography (PPG). I. INTRODUCTION A. BACKGROUND AND MOTIVATION

Although wrist-type photoplethysmographic (hereafter referred to as WPPG) sensor signals can measure heart rate quite conveniently, the subjects’ hand movements can cause strong motion artifacts, and then the motion artifacts will heavily contaminate WPPG signals. Hence, it is challenging for us to accurately estimate heart rate from WPPG signals during intense physical activities. The WWPG method has attracted more attention thanks to the popularity of wrist-worn wearable devices. In this paper, a mixed approach called Mix-SVM is proposed, it can use multi-channel WPPG sensor signals and simultaneous acceleration signals to measurement heart rate. Firstly, we combine the principle component analysis and adaptive filter to remove a part of the motion artifacts. Due to the strong relativity between motion artifacts and acceleration signals, the further denoising problem is regarded as a sparse signals reconstruction problem. Then, we use a spectrum subtraction method to eliminate motion artifacts effectively. Finally, the spectral peak corresponding to heart rate is sought by an SVM-based spectral analysis method. Through the public PPG database in the 2015 IEEE Signal Processing Cup, we acquire the experimental results, i.e., the average absolute error was 1.01 beat per minute, and the Pearson correlation was 0.9972. These results also confirm that the proposed Mix-SVM approach has potential for multi-channel WPPG-based heart rate estimation in the presence of intense physical exercise.

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