  Energy-based ultrasound elastography techniques minimize a regularized cost
function consisting of data and continuity terms to obtain local displacement
estimates based on the local time-delay estimation (TDE) between
radio-frequency (RF) frames. The data term associated with the existing
techniques takes only the amplitude similarity into account and hence is not
sufficiently robust to the outlier samples present in the RF frames under
consideration. This drawback creates noticeable artifacts in the strain image.
To resolve this issue, we propose to formulate the data function as a linear
combination of the amplitude and gradient similarity constraints. We estimate
the adaptive weight concerning each similarity term following an iterative
scheme. Finally, we optimize the non-linear cost function in an efficient
manner to convert the problem to a sparse system of linear equations which are
solved for millions of variables. We call our technique rGLUE: robust data term
in GLobal Ultrasound Elastography. rGLUE has been validated using simulation,
phantom, in vivo liver, and breast datasets. In all of our experiments, rGLUE
substantially outperforms the recent elastography methods both visually and
quantitatively. For simulated, phantom, and in vivo datasets, respectively,
rGLUE achieves 107%, 18%, and 23% improvements of signal-to-noise ratio (SNR)
and 61%, 19%, and 25% improvements of contrast-to-noise ratio (CNR) over GLUE,
a recently-published elastography algorithm.
