Using Kalman Filter to Improve the Accuracy of Diffusion Coefficients in MR Imaging: A Simulation Study


avatar Sam Sharifzadeh Javidi 1 , 2 , * , avatar Hamidreza Saligheh Rad 1 , 2

Physics and Medical Engineering Department, Medicine School, Tehran University of Medical Sciences, Tehran, Iran
Quantitative Medical Imaging Systems Group, Research Center for Molecular and Cellular Imaging, Tehran University of Medical Sciences, Tehran, Iran

how to cite: Sharifzadeh Javidi S, Saligheh Rad H. Using Kalman Filter to Improve the Accuracy of Diffusion Coefficients in MR Imaging: A Simulation Study. Innov J Radiol. 2019;16(Special Issue):e99153.



The diffusion coefficient of water molecules in different tissues is a biomarker to diagnose and differentiate diseases, tumors, injuries, etc.. Using a motion-sensitizing gradient, it is possible to map the diffusion coefficient into diffusion-weighted MRI (DWI). Although DWI is a good tool for diagnosing, its accuracy in low regime SNR and even especially in high blood consumer organs is in question.


We aimed to improve the accuracy of the diffusion coefficient, especially in the presence of noise.


Diffusion of water molecules at each voxel causes a signal intensity decay that can be measured using a motion-sensitizing gradient. Blood perfusion in capillary network artifacts and measurement noise can affect the real amount of D. In light of considering process noise and measurement noise, Kalman filter is used to cancel perfusion artifacts and measurement noise. Based on the diffusion model (S = S0 exp (-b D)), signal intensity was produced several times and a complex Gaussian noise was added to it. Using a Kalman filter, a noise cancelation process was designed to improve the quality of results. The Kalman filter solved a linear problem in the form of state space. Therefore, the diffusion model was rewritten as log(S/S0)/-b = D in state space. The Kalman filter predicted the amount of D and then modified it based on measurements iteratively (Figure 1). Finally, the results of the proposed method and conventional method were compared with true values (Figure 2).


Statistical tests showed that the proposed method was significantly better than the conventional method (P < 0.01). The conventional method caused a bias in the results of DWI due to eliminating micro-vessel perfusion in the capillary network. However, Kalman filter could consider the effects of microvessel perfusion as a process noise and reduce its effects on results. Kalman filter results (Table 1) were compared with true values and the t-test showed no significant alteration (P = 0.25). Conventional method results were significantly different from true values and Kalman filter results (P < 0.0001).


Diffusion coefficients in the presence of noise and capillary network suffer from bias; however, the proposed method can be used in these situations to improve the quality of DWI images.

To see figures, table, and references, please refer to the PDF file.

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