Improved visualization and quantification of 4D flow MRI data using divergence-freewavelet denoising

4D flow MRI is a promising method for providing global quantification of cardiac flow in a single acquisition, yet its use in clinical application suffers from low velocity-to-noise ratio. In this work, we present a novel noise reduction processing for 4D flow MRI data using divergence-free wavelet transform. Divergence-free wavelets have the advantage of enforcing soft divergence-free conditions when discretization and partial voluming result in numerical non-divergence-free components and at the same time, provide sparse representation of flow in a generally divergence-free field. Efficient denoising is achieved by appropriate shrinkage of divergence-free and non-divergence-free wavelet coefficients. To verify its performance, divergence-free wavelet denoising was performed on simulated flow and compared with existing methods. The proposed processing was also applied on in vivo data and was demonstrated to improve visualization of flow data while preserving quantifications of flow data.