## 1 Introduction  
Intravoxel Incoherent Motion (IVIM) Magnetic Resonance Imaging (MRI) is a type of Diffusion-Weighted MRI (DW-MRI) acquisition, firstly proposed by [PERSON] et al. [1], for estimating diffusion and perfusion tissue properties. In the IVIM mathematical representation, a bi-exponential function of the diffusion signal decay at different \(b\)-values is used to simultaneously characterize tissue diffusivity and perfusion within capillaries. Specifically, the IVIM model allows us to estimate the diffusion (\(D\)) and pseudo-diffusion coefficients (\(D^{*}\)), along with the perfusion volume fraction (\(f\)) within the tissue. IVIM has gained particular interest in oncologic applications, especially in the last decade, thanks to the advancements in MRI hardware, pulse design and post-processingmethods [2]. In fact, recent works have proposed the adoption of the IVIM model to improve tumor diagnosis [3], prognosis [4] and response to treatment [5]. Furthermore, IVIM has also been used to characterize radiation-induced modifications in normal tissues after radiotherapy [6]. Nevertheless, the use of the IVIM technique is not confined to oncology, but it has significant potential in clinical and preclinical applications for neurological diseases [7] and other physio-pathological conditions [8; 9]. However, IVIM coefficient estimation presents several issues related to the presence of noise over the image, the correct model identification and the amount of tissue perfusion [10]. Currently, the most popular techniques to fit IVIM data are (i) the non-linear least-square (LSQ) fitting, based on the Levenberg-Marquardt algorithm [11], and (ii) the Bayesian approach, which provides the posterior probability densities of the coefficients based on prior knowledge [12]. The Bayesian method showed superior performance in reducing errors and variability [12], and also allowed the inclusion of a spatial dependence between voxels, to obtain more regular maps. This is the case of the spatial homogeneity prior [13] and the Conditional Auto-Regressive (CAR) prior specification, which takes into account information from the neighbor voxels [14; 15]. In particular, it was reported that the CAR specification on a segmented Bayesian method improved the estimation accuracy compared to both LSQ and traditional Bayes approaches, especially for \(D^{*}\)[15]; however, a limitation of the CAR method lies in the choice of the neighborhood, as it attributes the same weight to all surrounding voxels without considering the continuity of the structure. This leads to a slight decrease in the quality of the IVIM coefficient maps, especially at the tissue/tissue and tissue/background interfaces, characterized by a blotchy appearance. The goal of this work was to overcome this limitation by coupling the CAR prior with a \(k\)-means clustering approach, which distinguishes the different structures based on the diffusion signal decay along the \(b\)-values, and uses this information to set different weights to the contributions of the different neighbor voxels. This technological improvement was aimed to obtain more regular and reliable IVIM parametric maps. The voxel-based estimation of IVIM coefficients can be used in the clinical practice for the characterization of microstructural properties of diffusion and perfusion within subregions of organs/structures. This information can be useful, for example, to define prediction models for treatment response in oncology or to assess changes occurring in physiological and pathological conditions in different applications; therefore, the availability of high quality and accurate maps represents a paramount condition in clinical practice and improved quality maps may have, prospectively, an impact on the quality of care  
The proposed method was compared to the original CAR approach and a state-of-the-art Bayesian algorithm in terms of accuracy and map homogeneity. First, it was applied to a set of simulated phantoms for which the true value of the IVIM coefficients was known.