## 3 Results  
### Simulated Data  
The qualitative comparison of the estimated maps among the three different methods revealed that the CAR clustering approach was able to improve their quality with respect to the Bayesian CAR method without clustering and the state-of-the-art Bayesian approach without CAR (Figure 2).  
The Bayesian estimation without CAR generated maps with high contrast between different structures, but maintained a certain level of noise throughout the image, especially at low \(SNR\) values. On the contrary, the CAR approach without clustering was able to generate homogeneous values within the ROIs, but at the same time it lost the boundaries between the regions and introduced blurring and blotchy artifacts, especially at low \(SNR\) values and for \(D^{*}\). Instead, the proposed approach with clustering better highlighted the contrast between structures at the interfaces, and preserved a high homogeneity within the regions; therefore, it retained the advantages of both other methods.  
The error \(\varepsilon\) maps reported in Figure 3 make it evident that the high errors at the boundaries of the structures in the CAR maps were almost completely eliminated with the clustering approach, especially for high \(SNR\) values. In addition, it can be seen from the maps that, in both CAR approaches, \(\varepsilon\) values were highly dependent on the IVIM coefficient values (i.e., some specific triplets were more difficult to be estimated), whilst the Bayesian method without CAR seemed less dependent. In particular, it showed for \(D\) the same error level throughout the whole image.  
Figure 4 shows for each \(SNR\) the barplots of \(\varepsilon\) and \(CV\) averaged on the simulated images with the corresponding significance, while the detailed results for each specific simulation are reported in the Supplementary Materials Tables S1-S4. Similar trends of \(\varepsilon\) and \(CV\) can be observed for the three methods, with higher values at low \(SNR\) that decrease at high \(SNR\), as expected. The accuracy was generally higher under the proposed approach with clustering as regards the estimation of \(D\) and \(f\): \(\varepsilon\) on \(D\) presented an averaged reduction of 46% compared to the other approaches, which was significant for \(SNR=10\), \(SNR=100\) and \(SNR=200\); \(\varepsilon\) on \(f\) reduced of 21% compared to the Bayesian approach without CAR and of 34% compared to the CAR without clustering, although this was not statistically significant. As for \(D^{*}\), similar errors were obtained for both CAR approaches, lower than for Bayesian approach without CAR (non-significant reduction of about 58%). \(CV\) was always the lowest for the proposed approach with the clustering, for each IVIM coefficient and \(SNR\) value. Specifically, the introduction of clustering reduced the \(CV\) of about 25-55% compared to traditional Bayes, and of about 30% compared to the original  
Figure 2: Parametric maps of \(D\) (**a**), \(f\) (**b**) and \(D^{*}\) (**c**), estimated from a simulated image using the three methods (columns) at different \(SNR\) values (rows). The true maps are also reported in the top left corner.  
CAR approach. Furthermore, for \(D^{*}\) maps at low \(SNR\), the two CAR approaches presented similar \(CV\)s, and a significant reduction was found only between the original Bayesian approach without CAR and the CAR with clustering. On the contrary, for high \(SNR\) the original CAR without clustering and the traditional Bayesian approach were almost comparable, whilst the introduction of clustering significantly reduced the \(CV\) compared to both of them; therefore, the CAR with clustering was able to improve not only the quality of the maps, especially on the boundaries of the structures, but also the estimation of the IVIM coefficients with respect to the other methods.