Fig. 3.
Image reconstruction using locally low rank approach followed by Bayesian multipoint unfolding. a) A locally low-rank approach is employed for each velocity encoding separately. The locally low-rank model divides the image into 3-dimensional patches. Each patch is reordered into local Casorati matrices for which a low rank is enforced by penalizing the nuclear norm. Compared to a global Casorati matrix, the values of the singular values decrease more rapidly. b) Following reconstruction of the individual velocity encodings, for each Cartesian direction the different velocity encodings kv are combined using a Bayesian multipoint approach. A Bayesian probability model [4] provides posterior probabilities for mean velocity v and intra-voxel standard deviation σ given the measured signal S. v and σ are chosen such that the posterior probability is maximized, providing maps of turbulent kinetic energy (TKE) and mean velocities