Highly Undersampled 3D Golden Ratio Radial Imaging with Iterative Reconstruction

IntroductionCompressed Sensing (CS) [1,2] suggests that using nonlinear reconstruction algorithms based on convexoptimization an accurate signal reconstruction can be obtained from a number of samples much lower thanrequired by the Nyquist limit. Recently, CS was demonstrated for MR imaging from undersampled data [3, 4].Prerequisites for a good image reconstruction are the image compressibility and the incoherence of the samplingscheme. To exploit the full potential of CS, measurement samples should be acquired at random. However,random sampling of the k-space is generally impractical. Variable density sampling schemes (radial, spiral) lead toincoherent aliasing and are also advantageous because of their higher sampling density about the k-space origin,where most of the signal energy is contained. 3D variable density sampling is potentially appropriate for CS,because the noise-like aliasing is distributed within the complete volume, allowing high undersampling factors.Image reconstruction from a low number of measurements could be very useful for dynamic 3D imaging, toreduce the often long acquisition times and thus improve temporal resolution in 3D MRI.In this work, we demonstrate the applicability of CS for 3D dynamic imaging using highly undersampled 3Dradial acquisition with golden ratio profile ordering [5,6].