Direct mean strain estimation for elastography using nearest-neighbor weighted least-squares approach in the frequency domain

Abstract

Ultrasound elastography is emerging with enormous potential as a medical imaging modality for effective discrimination of pathological changes in soft tissue. It maps the tissue elasticity or strain due to a mechanical deformation applied to it. The strain image most often calculated from the derivative of the local displacement field is highly noisy because of the de-correlation effect mainly due to unstable free-hand scanning and/or irregular tissue motion; consequently, improving the SNR of the strain image is still a challenging problem in this area. In this paper, a novel approach using the nearest-neighbor weighted least-squares is presented for direct estimation of the 'mean' axial strain for high quality strain imaging. Like other time/frequency domain reported schemes, the proposed method exploits the fact that the post-compression rf echo signal is a time-scaled and shifted replica of the pre-compression rf echo signal. However, the elegance of our technique is that it directly computes the mean strain without explicitly using any post filter and/or previous local displacement/strain estimates as is usually done in the conventional approaches. It is implemented in the short-time Fourier transform domain through a nearest-neighbor weighted least-squares-based Fourier spectrum equalization technique. As the local tissue strain is expected to maintain continuity with its neighbors, we show here that the mean strain at the interrogative window can be directly computed from the common stretching factor that minimizes a cost function derived from the exponentially weighted windowed pre- and post-compression rf echo segments in both the lateral and axial directions. The performance of our algorithm is verified for up to 8% applied strain using simulation and experimental phantom data and the results reveal that the SNR of the strain image can be significantly improved compared to other reported algorithms in the literature. The efficacy of the algorithm is also tested with in vivo breast data known to have malignant or benign masses from histology.