Variance controlled shear stiffness images for MRE data

In the Magnetic Resonance Elastography experiment we consider a harmonically oscillating mechanical force applied to the boundary surface of a phantom and synchronized with the motion encoding gradient. The phantom is symmetric in the direction of the applied mechanical force and the vector component in that direction decouples from the other components and satisfies a Helmholtz equation. We present a local inversion method to determine the shear wave speed that: (1) treats the phase and amplitude of the data differently; (2) computes derivatives of the data by using statistically justified filtering; and (3) varies filters according to SNR. We test our methods on data from Mayo Clinic and recover the position and stiffness of a 3mm diameter inclusion.