Theoretical bounds on strain estimation in elastography

TLDR: An expression for the lower bound for the strain estimation error (LBSE) is obtained, derived under the assumption that the post-compression echo signal can be reconstructed to the original shape of the echo signal before compression.

Abstract: Elastography is a technique for the estimation of tissue elasticity that is based on the estimation of strain. Tissue strain can be estimated by finite difference computations of echo time-delay. Echo time-delays are obtained by cross-correlation processing of pre- and post-compression echo signals. Errors in strain estimation can be expressed in terms of the errors in time delay estimation for given echo-signal characteristics. The smallest time delay estimation error is given by the Cramer-Rao Lower Bound (CRLB), which can be achieved when operating under the small error condition. Based on the CRLB, we obtain an expression for the lower bound for the strain estimation error (LBSE). The LBSE equation is derived under the assumption that the post-compression echo signal can be reconstructed to the original shape of the echo signal before compression. The theoretical bound given by the LBSE may or may not be achievable in practice, depending on the compliance with the requirements for echo signal reconstruction. In an example, the obtained LBSE shows that there is potential for significant reduction of the current level of noise in elastograms. >