## 4 Discussion and Conclusions
It is worth noticing that a simpler clustering approach based only on the anatomical information brought by the image at \(b=0\) was not sufficient to reduce the blurring effects, since it is not able to capture tissue-specific differences in the diffusion signal decay. This also shows that a manual clustering is rather impossible for this problem, as it should require to analyze \"as a whole\" the entire set of images at different \(b\)-values, which is a very difficult task for a human operator. In fact, no work in the literature considers this manual procedure on diffusion signal dynamic. As the \(k\)-means requires to enter the number \(N_{\mathcal{C}}\) of clusters as input, we performed a preliminary sensitivity analysis on a subset of data. We found that the clusters usually remain quite invariant within the region of interest, while additional clusters are identified in the background. In the real images, we also found that for \(N_{\mathcal{C}}>9\) different clusters \(\mathcal{C}_{ij}\) are assigned to voxels in regions disjoint from each other, which belong to the same cluster for \(N_{\mathcal{C}}=9\), while the shape of the connected regions in the clusters does not change. Since the CAR prior is not affected by this difference, we have chosen to limit the number of clusters to 9. On the contrary, on real images, a lower number of clusters may not be able to satisfactorily reduce the blotchy effect produced by the original CAR approach. Results on simulated data have confirmed that the improved approached based on the clustering is able to face the CAR limitations, showing less noisy IVIM maps and sharper boundaries definition at the interfaces between structures, associated with reduced errors at the boundaries. In addition, comparable results were obtained from simulations generated at different \(b\)-values, considering both HN and pelvic setups. The application to some illustrative real oncologic cases has highlighted that the introduction of the clustering did not alter the IVIM maps estimation obtained by the original CAR method, with the advantage of reducing the typical blotchy appearance at the boundaries, which usually affects the CAR approach, especially at low \(SNR\)s and for the estimation of \(D^{*}\). The proposed method was able to generate IVIM maps with lower errors and higher quality compared to the original CAR and also to the standard Bayesian approach. Compared to other approaches that adopted a spatial homogeneity prior [13], the results with the CAR approach were similar in terms of map quality and accuracy, as already discussed in [15]. Even if a fair direct quantitative comparison between these works is not possible, it seems that the introduction of clusters in the CAR prior may give more regularized maps than those presented in [13], at least for simulated images. Recently, approaches based on deep neural networks (DNNs) have been introduced to estimate IVIM parametric maps [22; 23; 24]. In these works, it was reported a higher quality of the maps compared to those estimated using traditional least squared and Bayesian methods. Specifically, [PERSON] et al. [23] stated that an optimized DNN can improve IVIM estimation for tissues with low perfusion and on images with low \(SNR\), and generate less noisy maps with more robust estimation over neighbor voxels. In our work, we have not compared our method with DNN-based approaches; however, we are confident that our results are in line with those reported in [22; 23; 24]. In fact, thanks to the introduction of a spatial dependency through the CAR prior specification, the continuity between adjacent voxels that share the same diffusion and perfusion properties was guaranteed. Furthermore, our estimation accuracy was high even at very low \(SNR\), probably comparable with that obtained by DNNs (a direct comparison is not possible, as different setups and simulations were adopted).