The electrocardiogram (ECG) is a reliable tool for monitoring cardiac conditions non-invasively. Its use is nowadays widespread and extends beyond purely medical purposes. Nevertheless, its application in residential settings comes with drawbacks. Non-stationary noise caused by motion reduces the signal's quality and alters the signal's characteristics. In this paper, we employ canonical polyadic decomposition (CPD) along with the measurements of a 3D accelerometer to characterize and remove artifacts. A CPD decomposes a noisy ECG into its constituting elements by examining multi-dimensional correlations. Its success, however, depends on how well the constituting elements are estimated to configure the model. The purpose of this paper is to achieve this task. We recorded data from ten healthy subjects undertaking different movement types: Standing up, bending forward, walking, running, jumping, and climbing stairs. In addition, we recorded isolated motion artifacts from the back of the subjects and mixed them with the ECG signals. To quantify the performance of the decomposition process, we compared the difference in the signal-to-noise ratio (SNR) and the root mean squared error (RMSE) between the actual and the estimated ECG. The proposed CPD model outperforms the adaptive filter and the wavelet denoising in terms of the SNR.