Theoretical derivation of SNR, CNR and spatial resolution for a local adaptive strain estimator for elastography

Conventional techniques in elastography estimate the axial strain as the gradient of the displacement (time-delay) estimates obtained using cross-correlation of pre- and temporally stretched postcompression radiofrequency (RF) A-line segments. The use of a constant stretch factor for stretching the postcompression A-line is not adequate in the presence of heterogeneous targets that are commonly encountered. This led to the development of several adaptive strain estimation techniques in elastography. Yet, a theoretical framework for the image quality of adaptive strain estimation has not been established. In this work, we develop theoretical expressions for the image quality [measured in terms of the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and spatial resolution] of elastograms obtained using an adaptive strain estimator developed by Alam et al. (1998). We show a linear trade-off between the SNR and axial resolution of the strain elastogram with respect to the window length used for strain estimation. The CNR shows a quadratic tradeoff with the axial resolution with respect to the window length. The SNR, CNR and axial resolution are shown to improve with the ultrasonic bandwidth.