Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting.

High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times. Here we present a novel compressed sensing (CS) reconstruction approach using shearlets as a sparsifying transform allowing for fast 3D CMR (3DShearCS) using 3D radial phase encoding (RPE). An iterative reweighting scheme was applied during image reconstruction to ensure fast convergence and high image quality. Shearlets are mathematically optimal for a simplified model of natural images and have been proven to be more efficient than classical systems such as wavelets. 3DShearCS was compared to three other commonly used reconstruction approaches. Image quality was assessed quantitatively using general image quality metrics and using clinical diagnostic scores from expert reviewers. The proposed technique had lower relative errors, higher structural similarity and higher diagnostic scores compared to the other reconstruction techniques especially for high undersampling factors, i.e. short scan times. 3DShearCS provided ensured accurate depiction of cardiac anatomy for fast imaging and could help to promote 3D high-resolution CMR in clinical practice.