Noise analysis and improvement of displacement vector estimation from angular displacements

Elastography or elasticity imaging techniques typically image local strains or Young's modulus variations along the insonification direction. Recently, techniques that utilize angular displacement estimates obtained from multiple angular insonification of tissue have been reported. Angular displacement estimates obtained along different angular insonification directions have been utilized for spatial-angular compounding to reduce noise artifacts in axial-strain elastograms, and for estimating the axial and lateral components of the displacement vector and the corresponding strain tensors. However, these angular strain estimation techniques were based on the assumption that noise artifacts in the displacement estimates were independent and identically distributed and that the displacement estimates could be modeled using a zero-mean normal probability density function. Independent and identically distributed random variables refer to a collection of variables that have the same probability distribution and are mutually independent. In this article, a modified least-squares approach is presented that does not make any assumption regarding the noise in the angular displacement estimates and incorporates displacement noise artifacts into the strain estimation process using a cross-correlation matrix of the displacement noise artifacts. Two methods for estimating noise artifacts from the displacement images are described. Improvements in the strain tensor (axial and lateral) estimation performance are illustrated utilizing both simulation data obtained using finite-element analysis and experimental data obtained from a tissue-mimicking phantom. Improvements in the strain estimation performance are quantified in terms of the elastographic signal-to-noise and contrast-to-noise ratios obtained with and without the incorporation of the displacement noise artifacts into the least-squares strain estimator.