T-wave alternans (TWA) is a cardiac phenomenon that appears in the electrocardiogram (ECG) and is associated with the mechanisms leading to sudden cardiac death (SCD). In this study, we propose the use of a multilead TWA analysis scheme that combines the Laplacian likelihood ratio (LLR) method and periodic component analysis (piCA), an eigenvalue decomposition technique whose aim is to extract the most periodic sources of the signal. The proposed scheme is evaluated in different scenarios--from synthetic signals to stress test ECGs--and is compared to other reported schemes based on the LLR method. Results demonstrate that the piCA-based scheme provides a superior ability to detect TWA than previously reported schemes, and has the potential to improve the prognostic value of testing for TWA.