Three-Dimensional Compressed Sensing for Dynamic MRI

Introduction: Dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI) is a valuable tool used in a number of clinical applications. However, imaging of time-varying objects is a challenging task when both high spatial resolution and high temporal resolution is desired. It has been demonstrated that radial imaging techniques can yield increased temporal resolution without sacrificing spatial resolution and are less susceptible to motion [1,2]. However, highly undersampled radial trajectories result in increased streaking artifacts and low SNR. The recently introduced Compressed Sensing (CS) theory illustrates that a small number of linear measurements can be sufficient to reconstruct sparse or compressible signals [3,4] and has the potential to significantly accelerate data acquisition in MRI [5,6,7]. In this work, we introduce a CS theory based method for reconstruction of time-varying radial k-space data by exploiting the spatio-temporal sparsity of DCE-MRI images. Theory: Let us assume that we would like to reconstruct a dynamic object with N×N pixels at T time instances and that we will acquire L θ radial views at each time instance with Lr points along each radial line. Let f be the 2 N T dimensional vector representing the dynamic object being imaged, M the 2 r L L T N T θ × measurement matrix, and g a r L L T θ -dimensional vector of k-space measurements. Note that since we are interested in