Accurately estimating all strain components in quasi-static ultrasound elastography is crucial for the full analysis of biological media. In this study, 2D strain tensor imaging was investigated, focusing on the use of a regularization method to improve strain images. This method enforces the tissue property of (quasi-) incompressibility, while penalizing strong field variations, to smooth the displacement fields and reduce the noise in the strain components. The performance of the method was assessed with numerical simulations, phantoms, and in vivo breast tissues. For all the media examined, the results showed a significant improvement in both lateral displacement and strain, while axial fields were only slightly modified by the regularization. The introduction of penalty terms allowed us to obtain shear strain and rotation elastograms where the patterns around the inclusions/lesions were clearly visible. In phantom cases, the findings were consistent with the results obtained from the modeling of the experiments. Finally, the easier detectability of the inclusions/lesions in the final lateral strain images was associated with higher elastographic contrast-to-noise ratios (CNRs), with values in the range of [0.54–9.57] versus [0.08–0.38] before regularization.
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