Shear-modulus resolution implications of the Cramer-Rao bound for vibration elastography in isotropic soft tissues

This paper demonstrates that the Cramer-Rao bound provides clear answers to the question of how large the data window needs to be to obtain satisfactory quantitative estimates of shear modulus in vibration elastography of isotropic soft tissues. This leads to an elucidation of the tradeoff between resolution and noise in the reconstructed shear-modulus. Reconstruction gain is defined as the ratio of output signal-to-noise ratio on the shear modulus estimate to the input signal-to-noise on the displacement measurements. The optimal reconstruction gain is derived and found to be dependent on the number of samples per local wavelength as well as the local-window size. The bound demonstrates that adequate reconstructions should be possible using data covering only 1/30th of the local shear wavelength.