Gaussian Scale Mixture-Based Joint Reconstruction of Multicomponent MR Images from Undersampled K-Space Measurements

Xiaobo Qu¹, Changwei Hu², Di Guo¹, Lijun Bao², Zhong Chen²

Undersampling the measurement can reduce the acquisition time in magnetic resonance imaging (MRI) at the cost of introducing the aliasing artifacts. The sparsity of magnetic resonance (MR) images in wavelet transforms shows promising results to suppress these artifacts [1]. Recent developments demonstrate the Gaussian Scale Mixture (GSM) for modeling dependency of wavelet coefficients for single image can incorporate more prior information and improve the traditional wavelet-based reconstruction. In this paper, we consider the cases that MR study is comprised by many different types of images of the same patient (e.g. T1, T2, Proton density-PD, etc). By modeling the dependency of wavelet coefficients of these multi-component images as multicomponent GSM (mGSM), we propose an iterative algorithm to jointly reconstruct these MR images from undersampled k-space measurements. Simulation demonstrates that this model can improve the reconstructed MR images than the wavelet-based hard iterative thresholding separately does for each image.