The Intra-Voxel Incoherent Motion (IVIM) model is largely adopted to estimate slow and fast diffusion coefficients of water molecules in biological tissues, which are used in cancer applications. The most reported fitting approach is a voxel-wise segmented non-linear least square, whereas Bayesian approaches with a direct fit, also considering spatial regularization, were proposed too. In this work a novel segmented Bayesian method was proposed, also in combination with a spatial regularization through a Conditional Autoregressive (CAR) prior specification. The two segmented Bayesian approaches, with and without CAR specification, were compared with two standard least-square and a direct Bayesian fitting methods. All approaches were tested on simulated images and real data of patients with head-and-neck and rectal cancer. Estimation accuracy and maps noisiness were quantified on simulated images, whereas the coefficient of variation and the goodness of fit were evaluated for real data.Both versions of the segmented Bayesian approach outperformed the standard methods on simulated images for pseudo-diffusion (D * ) and perfusion fraction (f), whilst the segmented least-square fitting remained the less biased for the diffusion coefficient (D). On real data, Bayesian approaches provided the less noisy maps, and the two Bayesian methods without CAR generally estimated lower values for f and D * coefficients with respect to the other approaches.The proposed segmented Bayesian approaches were superior, in terms of estimation accuracy and maps quality, to the direct Bayesian model and the least-square fittings. The CAR method improved the estimation accuracy, especially for D * . KEYWORDS Bayesian Segmented Approach, Conditional Autoregressive Model, Diffusion-Weighted MRI, IVIM 1 INTRODUCTION Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is a non-invasive technique that quantitatively characterizes the diffusion properties of water molecules. 1 Typically, the standard analysis of DW-MRI signals provides the estimation of the Apparent Diffusion Coefficient (ADC), which is estimated using a mono-exponential decay model of the signal intensity over b values. The Intra-Voxel Incoherent Motion (IVIM) model describes the incoherent motion of the water molecules in function of diffusion and perfusionproperties of a tissue at the same time. 2 In the IVIM model, the signal intensity in each voxel is modeled via a bi-exponential decay over b, characterized by a first fast component, which is related to tissue perfusion (the blood flow in the capillaries), followed by a second slow component, which is related to tissue molecular diffusion. Specifically, the IVIM model allows to estimate the diffusion coefficient (D), the pseudo-diffusion coefficient (D * ) and the perfusion volume fraction (f) within the tissue. The estimation of these coefficients can be made within a region of interest, by averaging the signal intensities over the voxels, or voxel-by-voxel to obtain parametric maps.NMR in Biomedicine. 2020;33:e4201. wil...