Highly Undersampled 3D Golden Ratio Radial Imaging with Iterative Reconstruction

Introduction Compressed Sensing (CS) [1,2] suggests that using nonlinear reconstruction algorithms based on convex optimization an accurate signal reconstruction can be obtained from a number of samples much lower than required 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 sampling scheme. 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 to incoherent 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, to reduce 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 3D radial acquisition with golden ratio profile ordering [5,6]. Methods A 3D radial sequence [7] was applied that aims for a quasi-isotropic distribution of radial profiles in 3D k-space over the total duration of a scan as well as over an arbitrary time window extracted from a scan for dynamic imaging. This is achieved by using 2D golden ratios α = 0.4656 and β = 0.6823 [8] to calculate the increments Δkz = 2α and Δφ = 2πβ (Fig. 1) for successively measured projections. The isotropic distribution of profiles over time was used to perform dynamic imaging, by reconstructing images from small sections of the data (frames), during which dynamic changes are considered to be negligible. Conventional gridding reconstruction of undersampled 3D radial data often leads to images in which the imaged object is visible, but compromised by aliasing artifacts. To improve the image quality, images for each frame were iteratively reconstructed, solving the constrained optimization problem