Noise reduction in three-dimensional phase-contrast MR velocity measurements.

The authors have developed a method to reduce noise in three-dimensional (3D) phase-contrast magnetic resonance (MR) velocity measurements by exploiting the property that blood is incompressible and, therefore, the velocity field describing its flow must be divergence-free. The divergence-free condition is incorporated by a projection operation in Hilbert space. The velocity field obtained with 3D phase-contrast MR imaging is projected onto the space of divergence-free velocity fields. The reduction of noise is achieved because the projection operation eliminates the noise component that is not divergence-free. Signal-to-noise ratio (S/N) gains on the order of 15%-25% were observed. The immediate effect of this noise reduction manifests itself in higher-quality phase-contrast MR angiograms. Alternatively, the S/N gain can be traded for a reduction in imaging time and/or improved spatial resolution.