Principal Component Analysis Based on Scatter Matrices

Question

There is a paper on robust PCA based on scatter matrices: https://wis.kuleuven.be/statdatascience/robust/papers/2005/hubertrousseeuwvandenbranden-robpca-technom-2005.pdf. PCA is generally performed based on the covariance matrix. In heavy-tailed distributions, however, the second moment may not exist, that is, the population covariance matrix may not exist. In this case, can PCA be performed based on a scatter matrix? If so, what is the rationale for doing PCA with a scatter matrix in this case?