Figure 1.

The 3D q-aMRI algorithm pipeline begins with the decomposition of volumetric cine MRI using the 3D complex steerable pyramid. This process separates the images into various scales and orientations, isolating different spatial frequency components. The decomposed images are then split into amplitude and phase components, with the phases encoding information about sub-voxel motion. Next, the phase components are temporally filtered at each spatial location, orientation, and scale to enhance significant temporal changes. These filtered phases are split and proceed along two paths: the original amplification path for visualization and the quantification path for generating voxel displacement maps. For quantitative estimation, the data undergo the estimation of the spatial phase derivative. This involves estimating the spatial phase derivative from the decomposed image. The voxel displacement field is then calculated by solving a least squares optimization objective. This formula calculates the best-fit voxel displacement field that aligns the phase derivatives with the phase temporal changes. The color-coded images display the estimated voxel displacements in the axial (L/R direction, white arrow), sagittal (S/I direction, white arrow), and coronal (S/I direction, white arrow) planes. The plus sign indicates the positive direction of motion.