Using functional PCA for cardiac motion exploration

Principal component analysis (PCA) is a major tool in multivariate data analysis. Its paradigms are also used in Karhunen-Loeve decomposition, a standard tool in image processing. Extensions of PCA to the framework of functional data have been proposed. The analysis provided by functional PCA seems to be a powerful tool for finding principal sources of variability in curves or images, but fails to provide easy interpretations in the case of multifunctional data. Guidelines aiming at spot information from the outputs of PCA applied to functionals with values in the space of continuous functions upon a bounded domain are proposed. An application to cardiac motion analysis illustrates the complexity of the multifunctional framework and the results provided by functional PCA.