Bayesian reconstruction of DW-PROPELLER images using joint entropy

INTRODUCTION: Diffusion-weighted MRI (DWI) provides a non-invasive method for in vivo evaluation of tissue water mobility. Most DWI studies employ single-shot EPI techniques which can suffer severe artifacts and image distortion in some applications. Multi-shot FSE-based DW-PROPELLER (1) and Turboprop (2) have shown to overcome these limitations. However, the scan time is usually longer to achieve a good SNR. Although the speed can be improved by reducing the number of blades, noise will become an issue. In this abstract, we propose a novel Bayesian reconstruction method to reduce the number of blades without compromising the SNR. The method incorporates the information from high quality non-weighted images into the DWI reconstruction, with the joint entropy between the weighted and non-weighted image features as the prior. A non-parametric model is used for the joint probability density function, which is estimated from the two images. The method is shown to improve the DW image quality with a set of DWPROPELLER brain data. THEORY AND METHOD: DWI images exhibit strong correlations with the non-weighted images. When used in reconstruction, the correlations can significantly improve the image quality of DWI (3,4). However, the relationship is complex and indirect due to different contrasts. We propose to use joint entropy as a metric for the correlation, which has been validated as a correlation metric for PET and MRI features (5). Bayesian method (6) is employed to incorporate the correlation in reconstructing the DWI images. Specifically, the desired DW image v is reconstructed by the maximum a posteriori (MAP) estimation ) ( ) | ( max arg v p v m p v v = , where ) | ( v m p is the Gaussian likelihood function representing the measurement noise in m, and ) (v p is the prior. We