Schatten norms are often useful for convex relaxations for matrix factorisation problems. This paper proposes a so called Factor Group-Sparse Regularizers (FGSRs), that give an alternative formulation For certain Schatten-p norms, where p is small. These relaxations are claimed having useful properties: they are tighter surrogates for the rank than the nuclear norm and they can be optimized without an explicit SVD calculation (which can become quite prohibitive even if randomized methods are used). The authors also provide a computational study to demonstrate the effectiveness of the approach and illustrate that the method seem to perform well in in denoising and matrix completion tasks regardless of the initial choice of rank. The paper has a fine balance in theoretical and simulation study, and makes some interesting observations about FGSRs. Overall, the study is well executed and well reported. However, the topic is a well investigated one, so inevitably many interesting improvements become somewhat incremental, including the contributions of this paper.