Quantitative T1ρ imaging usually requires multiple spin-lock times to obtain T1ρ maps, which makes the acquisition time demanding especially for biexponential models. Compressed Sensing has demonstrated significant acquisition time reduction in MRI. Similar improvements are expected for T1ρ relaxation mapping, given the extensive correlations in the series of images. However, it is not clear which combination of sparsifying transform and regularization function performs best for biexponential T1ρ mapping. Here, we compare five CS approaches: l1-norm of principal component analysis, spatio-temporal finite differences, exponential dictionaries, low rank, and low rank plus sparse. Our preliminary results, with three datasets, suggest that L+S is the most suitable method with least T1ρ estimation error.