Estimation of undistorted images in brain echo‐planar images with distortions using the conjugate gradient method with anatomical regularization

<jats:title>Abstract</jats:title><jats:sec><jats:title>Purpose</jats:title><jats:p>Although echo‐planar imaging (EPI) is widely used for diffusion magnetic resonance (MR) imaging, EPI images suffer from susceptibility‐induced geometric distortions. We herein propose a new estimation method for undistorted EPI images using anatomical T<jats:sub>1</jats:sub>‐weighted images (T<jats:sub>1</jats:sub>WIs) based on the physics of MR imaging.</jats:p></jats:sec><jats:sec><jats:title>Methods</jats:title><jats:p>Our proposed method estimates the undistorted EPI image in the image domain while estimating the magnetic field inhomogeneity map using the conjugate gradient method with anatomical regularization. Our method synthesizes the distorted image to match the measured EPI image containing geometric distortions by alternately updating the undistorted EPI image and the magnetic field inhomogeneity map. We evaluated our proposed method and compared it with a nonrigid registration‐based distortion correction method using simulated data and using real data. In the evaluation of the estimation of the magnetic field inhomogeneity map, we used the normalized root‐mean‐squared error (NRMSE) between the estimated results and the ground truth. In the evaluation of the estimation of undistorted images, we used mutual information (MI) between the undistorted EPI image and the anatomical T<jats:sub>1</jats:sub>WI.</jats:p></jats:sec><jats:sec><jats:title>Results</jats:title><jats:p>Using the simulated data, the means and standard deviations of the NRMSE values in the nonrigid registration‐based method and proposed method were 1.29 ± 0.63 and 0.64 ± 0.30, respectively. The MI values in the proposed method were larger than those in the nonrigid registration‐based method in all evaluated slices. For the real data, the proposed method improved the distortion, and the MI values in the proposed method were larger than those in the nonrigid registration‐based method. In the estimation of the magnetic field inhomogeneity map, the NRMSE values in our method were smaller than those in the nonrigid registration‐based method.</jats:p></jats:sec><jats:sec><jats:title>Conclusions</jats:title><jats:p>We demonstrated that our proposed method can estimate the regions with compressed distortions that are not well represented by the nonrigid registration‐based methods. The results suggest that the proposed method could be useful in analyses combining EPI images with T<jats:sub>1</jats:sub>WIs.</jats:p></jats:sec>